A308866 a(n) = Sum_{k>=0} k^(2^n)/2^(k+1).

1, 3, 75, 545835, 5315654681981355, 23545154085734896649184490637144855476395, 1408419189834457368564204829523128565178390518208834734403870775971211916384631776000167564122146475

Offset: 0

Author

Ilya Gutkovskiy, Jun 29 2019

Keywords

• nonn

Crossrefs

Cf. A000079, A000670, A008277, A135085.

Programs

Mathematica

Table[Sum[k^(2^n)/2^(k + 1), {k, 0, Infinity}], {n, 0, 6}]
Table[Sum[k! StirlingS2[2^n, k], {k, 0, 2^n}], {n, 0, 6}]

Formula

a(n) = Sum_{k=0..2^n} k!*Stirling2(2^n,k).

a(n) = A000670(A000079(n)).