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%I #7 Jun 14 2018 09:11:15
%S 1,2,6,18,64,230,936,3822,17344,78354,389280,1913010,10267776,
%T 54235350,311348352,1751907150,10673326080,63531238050,408231498240,
%U 2556121021650,17236028160000,113006008398150,796296326031360,5445783239554350,39959419088977920,284127133728611250
%N a(n) = Sum_{k=0..n} binomial(n,k)*k!!*(n - k)!!.
%C Exponential convolution of A006882 with itself.
%H Alois P. Heinz, <a href="/A305578/b305578.txt">Table of n, a(n) for n = 0..730</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DoubleFactorial.html">Double Factorial</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>
%F E.g.f.: (1 + x*exp(x^2/2)*(1 + sqrt(Pi/2)*erf(x/sqrt(2))))^2.
%p a:= proc(n) option remember; `if`(n<4, [1, 2, 6, 18][n+1],
%p 3*n*a(n-2)-2*(n-3)*n*a(n-4))
%p end:
%p seq(a(n), n=0..30); # _Alois P. Heinz_, Jun 14 2018
%t Table[Sum[Binomial[n, k] k!! (n - k)!!, {k, 0, n}], {n, 0, 25}]
%t nmax = 25; CoefficientList[Series[(1 + x Exp[x^2/2] (1 + Sqrt[Pi/2] Erf[x/Sqrt[2]]))^2, {x, 0, nmax}], x] Range[0, nmax]!
%Y Cf. A000165, A001563, A002866, A006882, A305577.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Jun 05 2018
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