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%I #17 Oct 08 2017 18:09:12
%S 1,26,1636,191336,35909776,9877824416,3744949458496,1871860519454336,
%T 1192747133878118656,943718459840134969856,907745644208033315808256,
%U 1043182479702092427281524736,1411605714773024334343061671936
%N Sum of an infinite series: a(n) = Sum_{k>=0} ((k+1)*(k+2))^n/(16*(2^k)).
%F a(n) = (1/8)*Sum_{i=0..n} C(n, i)*A000629(n+i). - _Benoit Cloitre_, Feb 02 2003
%F a(n) ~ (2n)!/(4*sqrt(2)*(log(2))^(2*n+1)). - _Vaclav Kotesovec_, Jun 29 2013
%t Table[1/8*Sum[Binomial[n,i]*(n+i)!*SeriesCoefficient[Exp[x]/(2-Exp[x]),{x,0,n+i}],{i,0,n}],{n,1,20}] (* _Vaclav Kotesovec_ after _Benoit Cloitre_, Jun 29 2013 *)
%K nonn
%O 1,2
%A _Karol A. Penson_, Jan 31 2003
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