A192554 a(n) = Sum_{k=0..n} abs(Stirling1(n,k))*(-1)^(n-k)*k!^2.

1, 1, 3, 26, 398, 9724, 344236, 16663968, 1056631824, 84962783664, 8446120969104, 1016998946575776, 145848462866589600, 24562489788256472064, 4799789988678066147840, 1077128972416478325901824, 275111625956753684599202304

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..253

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k) * k!^2. - Vaclav Kotesovec, Jul 05 2021

a(n) ~ exp(-1/2) * n!^2. - Vaclav Kotesovec, Jul 05 2021

E.g.f.: Sum_{k>=0} k! * log(1+x)^k. - Seiichi Manyama, Apr 22 2022

Mathematica

Table[Sum[Abs[StirlingS1[n, k]](-1)^(n-k)k!^2, {k, 0, n}], {n, 0, 100}]
Table[Sum[StirlingS1[n, k] * k!^2, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 05 2021 *)

Prog

(Maxima) makelist(sum(abs(stirling1(n, k))*(-1)^(n-k)*k!^2, k, 0, n), n, 0, 24);
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, k!*log(1+x)^k))) \\ Seiichi Manyama, Apr 22 2022

Crossrefs

Cf. A006252, A320502, A351280.

Cf. A064618.

Sequence in context: A300283 A326431 A206403 * A306280 A305144 A206402

Adjacent sequences: A192551 A192552 A192553 * A192555 A192556 A192557

Keyword

nonn

Author

Emanuele Munarini, Jul 04 2011

Status

approved