A169619 Hankel transform of quartic (or 4-fold) factorial numbers A007696.

1, 4, 640, 11059200, 39749419008000, 48575443603606732800000, 29918051262318914110928977920000000, 12898757220773940360062849214160935321600000000000

Offset

0,2

Links

Table of n, a(n) for n=0..7.

Formula

a(n) = Product_{k=0..n} ((4*k+1)*(4*k+4))^(n-k).

a(n) ~ 2^(2*n^2 + 3*n + 5/8) * Pi^(n + 5/8) * n^(n^2 + 5*n/4 + 35/96) / (A^(7/8) * Gamma(1/4)^(n + 1/4) * exp(3*n^2/2 + 5*n/4 - 7/96 - G/(4*Pi))), where G is Catalan's constant A006752 and A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jan 23 2024

Mathematica

Table[Product[((4*k+1)*(4*k+4))^(n-k), {k, 0, n}], {n, 0, 10}] (* Vaclav Kotesovec, Jan 23 2024 *)

Crossrefs

Cf. A007696.

Sequence in context: A219892 A079103 A191953 * A337650 A091288 A067171

Adjacent sequences: A169616 A169617 A169618 * A169620 A169621 A169622

Keyword

easy,nonn

Author

Paul Barry, Dec 03 2009

Status

approved