A072598 - OEIS

A072598

a(n)= 3^(4*n-4)* Sum_{k>=0} ( Gamma(n+k/3+1/3) / Gamma(4/3+k/3) ) * (Gamma(n+k/3+2/3) / Gamma(5/3+k/3) ) * (Gamma(n+k/3+1) / Gamma(2+k/3) ) * Gamma(n+k/3+4/3) / ( Gamma(7/3+k/3) * k! *exp(1)).

%I #7 Oct 13 2024 17:42:31

%S 1,1961,22982765,897960515649,87104111341922641,

%T 17553971396873140572281,6522485663882405640795371581,

%U 4101670732571144797304609148820545,4092893743093429344164150395340192148609,6162975970715988703282664052430391759867866441

%N a(n)= 3^(4*n-4)* Sum_{k>=0} ( Gamma(n+k/3+1/3) / Gamma(4/3+k/3) ) * (Gamma(n+k/3+2/3) / Gamma(5/3+k/3) ) * (Gamma(n+k/3+1) / Gamma(2+k/3) ) * Gamma(n+k/3+4/3) / ( Gamma(7/3+k/3) * k! *exp(1)).

%C Gamma in the definition is the standard Capital-Greek-Gamma function.

%Y Cf. A072019, A072020.

%K nonn

%O 1,2

%A _Karol A. Penson_, Jun 23 2002

%E More terms from _Sean A. Irvine_, Oct 13 2024