A034908 One half of octo-factorial numbers.

1, 10, 180, 4680, 159120, 6683040, 334152000, 19380816000, 1279133856000, 94655905344000, 7761784238208000, 698560581438720000, 68458936980994560000, 7256647319985423360000, 827257794478338263040000, 100925450926357268090880000, 13120308620426444851814400000

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..333

Index entries for sequences related to factorial numbers.

Formula

2*a(n) = (8*n-6)(!^8) := product(8*j-6, j=1..n) = 2^n*A007696(n); compare with A007696(n) = (4*n-3)(!^4) := product(4*j-3, j=1..n).

E.g.f.: (-1+(1-8*x)^(-1/4))/2.

G.f.: x/(1-10x/(1-8x/(1-18x/(1-16x/(1-26x/(1-24x/(1-34x/(1-32x/(1-... (continued fraction). - Philippe Deléham, Jan 07 2012

From Amiram Eldar, Dec 20 2022: (Start)

a(n) = A084948(n)/2.

Sum_{n>=1} 1/a(n) = 2*(e/8^6)^(1/8)*(Gamma(1/4) - Gamma(1/4, 1/8)). (End)

Mathematica

Drop[With[{nn = 40}, CoefficientList[Series[(-1 + (1 - 8*x)^(-1/4))/2, {x, 0, nn}], x]*Range[0, nn]!], 1] (* G. C. Greubel, Feb 26 2018 *)

Prog

(PARI) my(x='x+O('x^30)); Vec(serlaplace((-1+(1-8*x)^(-1/4))/2)) \\ G. C. Greubel, Feb 26 2018
(Magma) [(&*[(8*k-6): k in [1..n]])/2: n in [1..30]]; // G. C. Greubel, Feb 26 2018

Crossrefs

Cf. A007696, A045755, A034909, A039410, A039411, A039412, A084948.

Sequence in context: A067416 A113671 A001762 * A030048 A318796 A054918

Adjacent sequences: A034905 A034906 A034907 * A034909 A034910 A034911

Keyword

easy,nonn

Author

Wolfdieter Lang

Extensions

Terms a(16) onward added by G. C. Greubel, Feb 26 2018

Status

approved