A276964 - OEIS

%I #20 Sep 27 2016 09:08:08

%S 1,3,39,949,36573,2029551,152451283,14840686449,1812664465209,

%T 270925848659323,48571769994336831,10276325760127883853,

%U 2531148652596607988629,717525135328209346300839,231804543407519025287933163

%N a(n) = A000262(n)*A000262(n+1).

%F Recurrence: (2*n+3)*a(n+3)-(2*n+3)*(3*n^2+19*n+29)*a(n+2)+(n+2)*(n+1)*(2*n+7)*(3*n^2+13*n+13)*a(n+1)-n*(n+1)^3*(n+2)^2*(2*n+7)*a(n) = 0.

%F Asymptotic: a(n) ~ (1/2)*exp(-2*n+2*sqrt(n)+2*sqrt(n+1)-1)*(475/(110592*n^(3/2))+9025/(21233664*n^2)-5/(24*sqrt(n))-35/(1152*n)+1)*n^(2*n+1/2).

%F a(n) ~ exp(-1 + 4*sqrt(n) - 2*n) * n^(2*n + 1/2)/2 * (1 + 19/(24*sqrt(n)) + 589/(1152*n)). - _Vaclav Kotesovec_, Sep 27 2016

%t Table[HypergeometricPFQ[{-n+1,-n},{},1]HypergeometricPFQ[{-n,-n-1},{},1],{n,0,100}]

%o (Maxima) makelist(hypergeometric([-n+1,-n],[],1)*hypergeometric([-n,-n-1],[],1),n,0,12);

%Y Cf. A000262, A105278, A008297, A276960.

%K nonn

%O 0,2

%A _Emanuele Munarini_, Sep 27 2016