A373856 a(n) = Sum_{k=1..n} k! * k^(2*n-1) * |Stirling1(n,k)|.

0, 1, 17, 1652, 474770, 301474214, 357901156354, 712632435944568, 2204970751341231816, 10017874331177386762512, 63973486554110386836270096, 554598491512901862814742673168, 6344773703149123365957506715989568, 93563015826037060521986513216617599504

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

E.g.f.: Sum_{k>=1} (-log(1 - k^2*x))^k / k.

Mathematica

nmax=13; Range[0, nmax]!CoefficientList[Series[Sum[(-Log[1 - k^2*x])^k / k, {k, nmax}], {x, 0, nmax}], x] (* Stefano Spezia, Jun 19 2024 *)

Prog

(PARI) a(n) = sum(k=1, n, k!*k^(2*n-1)*abs(stirling(n, k, 1)));

Crossrefs

Cf. A003713, A373855.

Cf. A220179, A242228, A373858.

Cf. A351136, A373861.

Sequence in context: A227887 A144571 A242228 * A222905 A071826 A055414

Adjacent sequences: A373853 A373854 A373855 * A373857 A373858 A373859

Keyword

nonn

Author

Seiichi Manyama, Jun 19 2024

Status

approved