A276964 a(n) = A000262(n)*A000262(n+1).

1, 3, 39, 949, 36573, 2029551, 152451283, 14840686449, 1812664465209, 270925848659323, 48571769994336831, 10276325760127883853, 2531148652596607988629, 717525135328209346300839, 231804543407519025287933163

Offset

0,2

Links

Table of n, a(n) for n=0..14.

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000262, A105278, A008297, A276960.

Sequence in context: A301585 A258923 A326271 * A367596 A353739 A274573

Adjacent sequences: A276961 A276962 A276963 * A276965 A276966 A276967

Keyword

nonn

Author

Emanuele Munarini, Sep 27 2016

Status

approved