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A351218
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a(n) = Sum_{k=0..n} (-k)^k * Stirling2(n,k).
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3
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1, -1, 3, -16, 121, -1181, 14114, -199543, 3257139, -60279214, 1247164055, -28525394481, 714681439212, -19465007759913, 572609747089735, -18093710202583480, 611202186074834221, -21979340746682042249, 838330656532184312218, -33803668628843391999843
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OFFSET
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0,3
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..400
Eric Weisstein's World of Mathematics, Lambert W-Function.
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FORMULA
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E.g.f.: 1/(1 + LambertW(exp(x) - 1)), where LambertW() is the Lambert W-function.
a(n) ~ (-1)^n * n^n / (sqrt(exp(1)-1) * (1 - log(exp(1)-1))^(n + 1/2) * exp(n)). - Vaclav Kotesovec, Feb 05 2022
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MAPLE
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b:= proc(n, m) option remember; `if`(n=0,
(-m)^m, m*b(n-1, m)+b(n-1, m+1))
end:
a:= n-> b(n, 0):
seq(a(n), n=0..20); # Alois P. Heinz, Jul 17 2022
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MATHEMATICA
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Table[Sum[(-1)^k * k^k * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 05 2022 *)
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PROG
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(PARI) a(n) = sum(k=0, n, (-k)^k*stirling(n, k, 2));
(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(1/(1+lambertw(exp(x)-1))))
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CROSSREFS
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Cf. A282190, A305981.
Sequence in context: A145158 A132070 A121629 * A200793 A141625 A053588
Adjacent sequences: A351215 A351216 A351217 * A351219 A351220 A351221
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KEYWORD
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sign
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AUTHOR
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Seiichi Manyama, Feb 05 2022
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STATUS
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approved
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