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A351181 a(n) = Sum_{k=0..n} k^(k+n) * Stirling2(n,k). 2
1, 1, 17, 826, 79107, 12553011, 2979141058, 988163147091, 436562014218313, 247800100563125728, 175732698005376526429, 152264214647249387402567, 158273183995563848011907696, 194391589002961482387840145341 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..13.

FORMULA

E.g.f.: Sum_{k>=0} (k * (exp(k*x) - 1))^k / k!.

a(n) ~ c * r^(2*n) * (1 + exp(1 + 1/r))^n * n^(2*n) / exp(2*n), where r = 0.942405403803582963024019065398882138211529545249588032669864757847... is the root of the equation r*(1 + exp(-1 - 1/r)) * LambertW(-exp(-1/r)/r) = -1 and c = 0.94346979328254581112250921799629823027437848684764713214690470878402... - Vaclav Kotesovec, Feb 18 2022

MATHEMATICA

a[0] = 1; a[n_] := Sum[k^(k + n) * StirlingS2[n, k], {k, 1, n}]; Array[a, 14, 0] (* Amiram Eldar, Feb 04 2022 *)

PROG

(PARI) a(n) = sum(k=0, n, k^(k+n)*stirling(n, k, 2));

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*(exp(k*x)-1))^k/k!)))

CROSSREFS

Cf. A108459, A229233, A229261, A282190, A308490.

Cf. A350722, A351180.

Sequence in context: A249459 A191963 A328138 * A351769 A139091 A262634

Adjacent sequences:  A351178 A351179 A351180 * A351182 A351183 A351184

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Feb 04 2022

STATUS

approved

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Last modified September 29 12:57 EDT 2022. Contains 357090 sequences. (Running on oeis4.)