A276964 a(n) = A000262(n)*A000262(n+1).
1, 3, 39, 949, 36573, 2029551, 152451283, 14840686449, 1812664465209, 270925848659323, 48571769994336831, 10276325760127883853, 2531148652596607988629, 717525135328209346300839, 231804543407519025287933163
Offset: 0
Keywords
Programs
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Mathematica
Table[HypergeometricPFQ[{-n+1,-n},{},1]HypergeometricPFQ[{-n,-n-1},{},1],{n,0,100}] -
Maxima
makelist(hypergeometric([-n+1,-n],[],1)*hypergeometric([-n,-n-1],[],1),n,0,12);
Formula
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.
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).
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