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%I #28 Dec 20 2022 03:50:02
%S 1,15,345,10695,417105,19603935,1078216425,67927634775,4822862069025,
%T 381006103452975,33147531000408825,3149015445038838375,
%U 324348590839000352625,36002693583129039141375,4284320536392355657823625,544108708121829168543600375,73454675596446937753386050625
%N One seventh of octo-factorial numbers.
%H G. C. Greubel, <a href="/A034975/b034975.txt">Table of n, a(n) for n = 1..325</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F 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)).
%F E.g.f.: (-1+(1-8*x)^(-7/8))/7.
%F 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
%F a(n) = (1/7) * 8^n * Pochhammer(n, 7/8). - _G. C. Greubel_, Oct 21 2022
%F From _Amiram Eldar_, Dec 20 2022: (Start)
%F a(n) = A049210(n)/7.
%F Sum_{n>=1} 1/a(n) = 7*(e/8)^(1/8)*(Gamma(7/8) - Gamma(7/8, 1/8)). (End)
%t Table[8^n*Pochhammer[7/8, n]/7, {n, 40}] (* _G. C. Greubel_, Oct 21 2022 *)
%o (Magma) [n le 1 select 1 else (8*n-1)*Self(n-1): n in [1..40]]; // _G. C. Greubel_, Oct 21 2022
%o (SageMath) [8^n*rising_factorial(7/8,n)/7 for n in range(1,40)] # _G. C. Greubel_, Oct 21 2022
%Y Cf. A007696, A034176, A034908, A034909, A034910, A034911, A034912, A034976, A045755, A049210.
%K easy,nonn
%O 1,2
%A _Wolfdieter Lang_
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