A351333 - OEIS

A351333

a(n) = Sum_{k=0..n} k! * (-k)^k * Stirling1(n,k).

1, -1, 9, -188, 7210, -442534, 39778322, -4926514200, 804271290024, -167367096770256, 43244394345493968, -13583108127289832592, 5097183064576208028096, -2252211248747050526401296, 1157380447302779717382178416, -684423139836843936246492092928

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..15.

FORMULA

E.g.f.: Sum_{k>=0} (-k * log(1+x))^k.

PROG

(PARI) a(n) = sum(k=0, n, k!*(-k)^k*stirling(n, k, 1));

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (-k*log(1+x))^k)))

CROSSREFS

Cf. A351280, A351334.

Sequence in context: A266496 A078101 A133556 * A196215 A196682 A124008

Adjacent sequences: A351330 A351331 A351332 * A351334 A351335 A351336

KEYWORD

sign

AUTHOR

Seiichi Manyama, Feb 07 2022

STATUS

approved