A100262 Expansion of A(x)^2, where A(x) = o.g.f. of n^n (A000312).

1, 2, 9, 62, 582, 6978, 102339, 1779222, 35809052, 819103178, 20987183525, 595341928814, 18519658804818, 626784970780690, 22926284614808071, 901188628763393606, 37882728189752349304, 1695744102631158083866

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..386

Thomas Wieder, The number of certain k-combinations of an n-set, Applied Mathematics Electronic Notes, vol. 8 (2008).

Formula

a(n) = Sum_{k=0..n} k^k * (n-k)^(n-k). - Tilman Neumann, Dec 13 2008

a(n) ~ 2 * n^n. - Vaclav Kotesovec, Dec 03 2021

Example

(1 + x + 4x^2 + 27x^3 + 256x^4 +...)^2 = 1 + 2x + 9x^2 + 62x^3 +...

Mathematica

nn=17; f[x_]=1+Sum[n^n x^n, {n, 1, nn}]; CoefficientList[Series[f[x]^2, {x, 0, nn}], x] (* Geoffrey Critzer, Nov 05 2013 *)

Prog

(PARI) a(n) = sum(k=0, n, k^k*(n-k)^(n-k)); \\ Seiichi Manyama, Dec 03 2021

Crossrefs

Cf. A000312, A053729, A062817, A349874.

Sequence in context: A352326 A052820 A213528 * A166886 A212413 A003577

Adjacent sequences: A100259 A100260 A100261 * A100263 A100264 A100265

Keyword

nonn

Author

Ralf Stephan, Nov 20 2004

Status

approved