A354002 Inverse Stirling transform of odd primes.

3, 2, -2, 6, -30, 192, -1440, 12240, -115916, 1209422, -13784264, 170426380, -2272355448, 32507854434, -496746974148, 8076163535824, -139211242006108, 2536169979011432, -48695473146705746, 982863502262307532, -20805668315828056010, 460926536131613987430

Offset

1,1

Links

Winston de Greef, Table of n, a(n) for n = 1..448

Formula

E.g.f.: Sum_{k>=1} prime(k+1) * log(1 + x)^k / k!.

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

Mathematica

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

Prog

(PARI) a(n) = sum(k=1, n, stirling(n, k, 1) * prime(k+1)); \\ Michel Marcus, May 13 2022

Crossrefs

Cf. A065091, A307772, A307773, A353406, A354003.

Sequence in context: A234713 A091029 A272372 * A280850 A296508 A299778

Adjacent sequences: A353999 A354000 A354001 * A354003 A354004 A354005

Keyword

sign

Author

Ilya Gutkovskiy, May 13 2022

Status

approved