A080163 Sum of an infinite series: a(n) = Sum_{k>=0} ((k+1)*(k+2))^n/(16*(2^k)).
1, 26, 1636, 191336, 35909776, 9877824416, 3744949458496, 1871860519454336, 1192747133878118656, 943718459840134969856, 907745644208033315808256, 1043182479702092427281524736, 1411605714773024334343061671936
Offset: 1
Keywords
Programs
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Mathematica
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 *)
Formula
a(n) = (1/8)*Sum_{i=0..n} C(n, i)*A000629(n+i). - Benoit Cloitre, Feb 02 2003
a(n) ~ (2n)!/(4*sqrt(2)*(log(2))^(2*n+1)). - Vaclav Kotesovec, Jun 29 2013