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URL: https://oeis.org/A034975

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A034975
One seventh of octo-factorial numbers.
6
1, 15, 345, 10695, 417105, 19603935, 1078216425, 67927634775, 4822862069025, 381006103452975, 33147531000408825, 3149015445038838375, 324348590839000352625, 36002693583129039141375, 4284320536392355657823625, 544108708121829168543600375, 73454675596446937753386050625
OFFSET
1,2
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
KEYWORD
easy,nonn
STATUS
approved