A307773 Expansion of e.g.f. Sum_{k>=1} prime(k)*log(1/(1 - x))^k/k!.

2, 5, 18, 82, 454, 2960, 22212, 188568, 1786896, 18698116, 214149822, 2664667358, 35796803068, 516387315172, 7961576156330, 130655542040262, 2273957872532176, 41836619073742452, 811316702293124504, 16540499893106494782, 353673865103189710572, 7914396129656344633522

Offset: 1

Author

Ilya Gutkovskiy, Apr 27 2019

Keywords

• nonn

Crossrefs

Cf. A000040, A307771, A307772.

Programs

Maple

a:= n-> add(ithprime(k)*abs(Stirling1(n, k)), k=1..n):
seq(a(n), n=1..30);  # Alois P. Heinz, Apr 27 2019

Mathematica

nmax = 22; Rest[CoefficientList[Series[Sum[Prime[k] Log[1/(1 - x)]^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!]
Table[Sum[Abs[StirlingS1[n, k]] Prime[k], {k, 1, n}], {n, 1, 22}]

Formula

a(n) = Sum_{k=1..n} |Stirling1(n,k)|*prime(k).