A351795 a(n) = n! * Sum_{k=0..n} (k * (n-k))^k/k!.

1, 1, 4, 30, 396, 8360, 256470, 10619952, 564959528, 37370475648, 3001942868490, 287388158562560, 32278318416029532, 4197544986996581376, 625014083479647028622, 105554855135062180485120, 20053957030647088382195280, 4255329207190209023134564352

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..266

Vaclav Kotesovec, Graph - the asymptotic ratio (10000 terms)

Formula

a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / (sqrt(LambertW(exp(2)*n)^2 - 1) * exp(n*(1 - 1/LambertW(exp(2)*n))) * LambertW(exp(2)*n)^n). - Vaclav Kotesovec, Feb 20 2022

Mathematica

a[n_] := n!*(1 + Sum[(k*(n - k))^k/k!, {k, 1, n}]); Array[a, 18, 0] (* Amiram Eldar, Feb 19 2022 *)

Prog

(PARI) a(n) = n!*sum(k=0, n, (k*(n-k))^k/k!);

Crossrefs

Cf. A235328, A349965, A351768, A351796.

Sequence in context: A199569 A363911 A326205 * A290058 A168129 A193500

Adjacent sequences: A351792 A351793 A351794 * A351796 A351797 A351798

Keyword

nonn

Author

Seiichi Manyama, Feb 19 2022

Status

approved