A034975 One seventh of octo-factorial numbers.

1, 15, 345, 10695, 417105, 19603935, 1078216425, 67927634775, 4822862069025, 381006103452975, 33147531000408825, 3149015445038838375, 324348590839000352625, 36002693583129039141375, 4284320536392355657823625, 544108708121829168543600375, 73454675596446937753386050625

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..325

Index entries for sequences related to factorial numbers.

Formula

7*a(n) = (8*n-1)!^8 = Product_{j=1..n} (8*j-1) = (8*n)!/((2*n)!*2^(6*n)*3^2*5 * A045755(n)*A007696(n)*A034909(n)*A034911(n)*A034176(n)).

E.g.f.: (-1+(1-8*x)^(-7/8))/7.

G.f.: x/(1-15*x/(1-8*x/(1-23*x/(1-16*x/(1-31*x/(1-24*x/(1-39*x/(1-32*x/(1-... (continued fraction). - Philippe Deléham, Jan 07 2012

a(n) = (1/7) * 8^n * Pochhammer(n, 7/8). - G. C. Greubel, Oct 21 2022

From Amiram Eldar, Dec 20 2022: (Start)

a(n) = A049210(n)/7.

Sum_{n>=1} 1/a(n) = 7*(e/8)^(1/8)*(Gamma(7/8) - Gamma(7/8, 1/8)). (End)

Mathematica

Table[8^n*Pochhammer[7/8, n]/7, {n, 40}] (* G. C. Greubel, Oct 21 2022 *)

Prog

(Magma) [n le 1 select 1 else (8*n-1)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 21 2022
(SageMath) [8^n*rising_factorial(7/8, n)/7 for n in range(1, 40)] # G. C. Greubel, Oct 21 2022

Crossrefs

Cf. A007696, A034176, A034908, A034909, A034910, A034911, A034912, A034976, A045755, A049210.

Sequence in context: A321850 A100875 A286391 * A012787 A216449 A030049

Adjacent sequences: A034972 A034973 A034974 * A034976 A034977 A034978

Keyword

easy,nonn

Author

Wolfdieter Lang

Status

approved