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A169619
Hankel transform of quartic (or 4-fold) factorial numbers A007696.
2
1, 4, 640, 11059200, 39749419008000, 48575443603606732800000, 29918051262318914110928977920000000, 12898757220773940360062849214160935321600000000000
OFFSET
0,2
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Dec 03 2009
STATUS
approved