A280100 a(n) = 4^(2*n) * (n!)^3 * (n+1)!.

1, 32, 12288, 21233664, 108716359680, 1304596316160000, 31560794080542720000, 1385645103312147578880000, 102160842176998016695664640000, 11916040631525048667382323609600000, 2097223151148408565459288955289600000000

Offset: 0

Author

Daniel Suteu, Dec 25 2016

Keywords

• nonn
• easy

Links

• Daniel Suteu, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A134374, A161736, A278145.

Programs

PARI

a(n) = 4^(2*n) * (n!)^3 * (n+1)!;

Formula

a(n) ~ Pi/4 * A134374(n).

a(n) ~ Pi^2 * 2^(4*n+2) / exp(4*n+1) * n^(3*n+3/2) * (n+1)^(n+3/2).

Lim_{n->infinity} a(n) / ((2n+1)!)^2 = Pi/4.

a(n) / ((2n+1)!)^2 = A278145(n) / A161736(n+2).