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A192554 a(n) = Sum_{k=0..n} abs(Stirling1(n,k))*(-1)^(n-k)*k!^2. 2
1, 1, 3, 26, 398, 9724, 344236, 16663968, 1056631824, 84962783664, 8446120969104, 1016998946575776, 145848462866589600, 24562489788256472064, 4799789988678066147840, 1077128972416478325901824, 275111625956753684599202304 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 23 23:07 EDT 2022. Contains 353993 sequences. (Running on oeis4.)