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
Keywords
Examples
(1 + x + 4x^2 + 27x^3 + 256x^4 +...)^2 = 1 + 2x + 9x^2 + 62x^3 +...
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).
Programs
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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 *) -
PARI
a(n) = sum(k=0, n, k^k*(n-k)^(n-k)); \\ Seiichi Manyama, Dec 03 2021
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