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A192554
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a(n) = Sum_{k=0..n} abs(Stirling1(n,k))*(-1)^(n-k)*k!^2.
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2
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1, 1, 3, 26, 398, 9724, 344236, 16663968, 1056631824, 84962783664, 8446120969104, 1016998946575776, 145848462866589600, 24562489788256472064, 4799789988678066147840, 1077128972416478325901824, 275111625956753684599202304
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OFFSET
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0,3
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LINKS
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Seiichi Manyama, Table of n, a(n) for n = 0..253
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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Cf. A006252, A320502, A351280.
Cf. A064618.
Sequence in context: A300283 A326431 A206403 * A306280 A305144 A206402
Adjacent sequences: A192551 A192552 A192553 * A192555 A192556 A192557
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KEYWORD
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nonn
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AUTHOR
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Emanuele Munarini, Jul 04 2011
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STATUS
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approved
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