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Sum_{k=0..n} k^(n-k)*(n+k)^k.
3

%I #5 Dec 20 2014 16:24:08

%S 2,19,270,5274,131250,3971953,141615782,5814096100,270145723914,

%T 14014491434175,802959561033630,50357860270776302,3431283333644097698,

%U 252413829036827831821,19937800344936448113750,1683065517269356710047112,151213514611062314791034874

%N Sum_{k=0..n} k^(n-k)*(n+k)^k.

%F a(n) ~ 2^n * n^n / (1-exp(-1/2)/2). - _Vaclav Kotesovec_, Dec 20 2014

%t Table[Sum[k^(n-k)*(n+k)^k, {k, 0, n}], {n, 1, 20}]

%Y Cf. A062817, A252708, A252709.

%K nonn,easy

%O 1,1

%A _Vaclav Kotesovec_, Dec 20 2014