A373858 - OEIS

A373858

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

0, 1, 15, 1268, 317294, 175542694, 181641609214, 315309390376056, 850661260866748728, 3370191684116333977872, 18768704088141613880906736, 141902519646656406912522712848, 1415862822521619228707500717132224, 18210234893009450819658863637633454608

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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)*stirling(n, k, 1));

CROSSREFS

Cf. A220179, A242228, A373856.

Cf. A351133, A351183.

Sequence in context: A273967 A273963 A220179 * A166330 A300618 A232147

Adjacent sequences: A373855 A373856 A373857 * A373859 A373860 A373861

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Jun 19 2024

STATUS

approved