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A080163 Sum of an infinite series: a(n) = Sum_{k>=0} ((k+1)*(k+2))^n/(16*(2^k)). 1
1, 26, 1636, 191336, 35909776, 9877824416, 3744949458496, 1871860519454336, 1192747133878118656, 943718459840134969856, 907745644208033315808256, 1043182479702092427281524736, 1411605714773024334343061671936 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..13.

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

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 *)

CROSSREFS

Sequence in context: A042303 A042300 A282884 * A300578 A217228 A005644

Adjacent sequences:  A080160 A080161 A080162 * A080164 A080165 A080166

KEYWORD

nonn

AUTHOR

Karol A. Penson, Jan 31 2003

STATUS

approved

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Last modified October 16 15:51 EDT 2019. Contains 328101 sequences. (Running on oeis4.)