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

%I A100262 #23 Dec 03 2021 09:54:47
%S A100262 1,2,9,62,582,6978,102339,1779222,35809052,819103178,20987183525,
%T A100262 595341928814,18519658804818,626784970780690,22926284614808071,
%U A100262 901188628763393606,37882728189752349304,1695744102631158083866
%N A100262 Expansion of A(x)^2, where A(x) = o.g.f. of n^n (A000312).
%H A100262 Seiichi Manyama, <a href="/A100262/b100262.txt">Table of n, a(n) for n = 0..386</a>
%H A100262 Thomas Wieder, The number of certain k-combinations of an n-set, <a href="http://www.math.nthu.edu.tw/~amen/">Applied Mathematics Electronic Notes</a>, vol. 8 (2008).
%F A100262 a(n) = Sum_{k=0..n} k^k * (n-k)^(n-k). - _Tilman Neumann_, Dec 13 2008
%F A100262 a(n) ~ 2 * n^n. - _Vaclav Kotesovec_, Dec 03 2021
%e A100262 (1 + x + 4x^2 + 27x^3 + 256x^4 +...)^2 = 1 + 2x + 9x^2 + 62x^3 +...
%t A100262 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 *)
%o A100262 (PARI) a(n) = sum(k=0, n, k^k*(n-k)^(n-k)); \\ _Seiichi Manyama_, Dec 03 2021
%Y A100262 Cf. A000312, A053729, A062817, A349874.
%K A100262 nonn
%O A100262 0,2
%A A100262 _Ralf Stephan_, Nov 20 2004