This is intended as a historical complement to the technical answers.
I'm aware of the treatment it is liable to receive.
I still believe it is worth posting.
Hopefully people will take it as a useful complement to the more pragmatic detailed material in other answers.
I write this in 2020.
75 years ago the US was just concluding part 2 of the-war-to-end-all-wars.
This had been intended to be a 1 part war but "things went wrong".
The thought of part 3 occurring at some future date was not to be countenanced.
There were strong opinions expressed in the US hierarchy that Germany should be not just demilitarised but deindustrialised - the Ruhr stripped of most of its factories and the nation rendered essentially pastoral. While this was neither the major or ultimately prevailing decision, it made sense enough at the time.
For those doubrful of these ideas or not familiar with "The Morgenthau Plan" a skim through this material should be instructive). (Morgenthau was Roosevelt's Secretary of the Treasury.)
Nobody, and that may well literally be nobody, would have imagined that well within 100 years the land of Naziism, the Third Reich, Lebensraum, concentration camps, ethic cleansing before it was a thing and so much more would ever take it's place as a willing and capable democratic partner in Western Europe. The idea of the US providing Germany with nuclear weapons for (potential) delivery by German pilots would have made 'Dr Strangelove' seem mild.
And yet, here we are.
In part 1 of the war-to-end-all-wars (to be continued) Canadian physician Lieutenant-Colonel John McCrae wrote a poem. We know it as "In Flanders Fields" It contains a passage intended as a challenge that instead became of such immense prophetic import that we read it and miss both what he was asking and what has been achieved.
Take up our quarrel with the foe:
To you from failing hands we throw
The torch; be yours to hold it high.
If ye break faith with us who die
We shall not sleep, though poppies grow
In Flanders fields.
Somewhat to my surprise, I often cry when I read this poem.
When McCRae wrote those words his idea of "take up our quarrel with the foe" meant just that. He would very much have agreed with the thoughts expressed in The MLF lullaby by the great Tom Lehrer - as noted and link supplied by Moshe Kohan in a comment.
And yet. Here we are.
After WW2 the threat posed by the Soviet Union, and the need to aid Europe lead, in an inseparable complex mix to "treating the vanquished well by any past standards, the Marshall plan and the cold war.
McCrae's challenge needed addressing.
The idea of round 3 of the war-to-end-all-wars popping up again as soon as the German's recovered their strength was beyond unacceptable. The Soviets provided the spur, if any was needed. Japan got massive US industrial advantage in the form of the one man army W.Edwards Deming. Germany got among other things, the Berlin Airlift (June 1948 May 1949) and support as a nation against the perils of the day. And it went from there.
McCrae's challenge was answered in a way which would have been beyond belief in 1945, and hardly more believable 3 years on as the US rallied to the support of their ally. (!).
What we see now is the logical conclusion of the path chosen then. Certainly, political relationships between German and the rest of Europe may often be "a little frayed". Even US - German relationships are not always as amicable as some would hope. But US nuclear weapons in German aircraft with German pilots (no matter how the actual lines of control may actually work) follow a progression expressed as a hope by a WW1 surgeon, fostered by Stalin as he sought to divide and conquer immediately post WW2, and ongoingly encouraged by the ongoing enmity between "The West" and The Soviet Union.
Arguably, no greater trust could be expressed in ones allies than to arm them with your own nuclear weapons, able to be delivered by their own pilots. It's logical. :-)