A336828 - OEIS

%I #15 Feb 20 2021 11:03:32

%S 1,1,8,108,2144,56250,1836792,71799504,3269445888,169974711630,

%T 9934458411800,644825382429096,46022332032100800,3582265183110626740,

%U 302002255041807372080,27413749834141448520000,2665789990569658618398720,276477318687585566522176470

%N a(n) = Sum_{k=0..n} binomial(n,k)^2 * k^n.

%H Seiichi Manyama, <a href="/A336828/b336828.txt">Table of n, a(n) for n = 0..343</a>

%F a(n) ~ c * d^n * (n-1)!, where d = (1 + 2*LambertW(exp(-1/2)/2)) / (4*LambertW(exp(-1/2)/2)^2) = 6.476217542109791521947605963458797355564... and c = 0.21617818094152997942246965143216887599763501682724844713834495... - _Vaclav Kotesovec_, Feb 20 2021

%t Join[{1}, Table[Sum[Binomial[n, k]^2 k^n, {k, 0, n}], {n, 1, 17}]]

%o (PARI) a(n) = sum(k=0, n, binomial(n, k)^2*k^n); \\ _Michel Marcus_, Aug 05 2020

%Y Cf. A000984, A002457, A037966, A037972, A072034, A074334, A187021, A329444, A329913, A336214, A341815.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Aug 05 2020