A362848 a(n) = Sum_{k=0..n} 4^k * Gamma(n + k + 1/2) / Gamma(n - k + 1/2). Row sums of A362847.

1, 4, 121, 11376, 2165689, 689873284, 330204013569, 221470234531456, 198160750081637521, 228040136335670652324, 328106086348844570538409, 577082259304437657893671984, 1218130815379359944856599793801, 3039062974890293661892991548863076

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = Sum_{k=0..n} (2*(n + k) - 1)!! / (2*(n - k) - 1)!!. - Detlef Meya, Oct 09 2023

a(n) ~ 2^(4*n + 1/2) * n^(2*n) / exp(2*n). - Vaclav Kotesovec, Oct 09 2023

Mathematica

a[n_]:= Sum[(2*(n+k)-1)!!/(2*(n-k)-1)!!, {k, 0, n}]; Flatten[Table[a[n], {n, 0, 13}]] (* Detlef Meya, Oct 09 2023 *)

Crossrefs

Cf. A362847.

Sequence in context: A358570 A263612 A033934 * A144508 A169972 A360664

Adjacent sequences: A362845 A362846 A362847 * A362849 A362850 A362851

Keyword

nonn

Author

Peter Luschny, May 05 2023

Status

approved