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 A351218 a(n) = Sum_{k=0..n} (-k)^k * Stirling2(n,k). 3
 1, -1, 3, -16, 121, -1181, 14114, -199543, 3257139, -60279214, 1247164055, -28525394481, 714681439212, -19465007759913, 572609747089735, -18093710202583480, 611202186074834221, -21979340746682042249, 838330656532184312218, -33803668628843391999843 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..400 Eric Weisstein's World of Mathematics, Lambert W-Function. FORMULA 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 MAPLE 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 MATHEMATICA Table[Sum[(-1)^k * k^k * StirlingS2[n, k], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Feb 05 2022 *) PROG (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)))) CROSSREFS Cf. A282190, A305981. Sequence in context: A145158 A132070 A121629 * A200793 A141625 A053588 Adjacent sequences: A351215 A351216 A351217 * A351219 A351220 A351221 KEYWORD sign AUTHOR Seiichi Manyama, Feb 05 2022 STATUS approved

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Last modified March 22 14:35 EDT 2023. Contains 361430 sequences. (Running on oeis4.)