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%I #36 Dec 20 2022 08:05:38
%S 1,10,180,4680,159120,6683040,334152000,19380816000,1279133856000,
%T 94655905344000,7761784238208000,698560581438720000,
%U 68458936980994560000,7256647319985423360000,827257794478338263040000,100925450926357268090880000,13120308620426444851814400000
%N One half of octo-factorial numbers.
%H G. C. Greubel, <a href="/A034908/b034908.txt">Table of n, a(n) for n = 1..333</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F 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).
%F E.g.f.: (-1+(1-8*x)^(-1/4))/2.
%F 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
%F From _Amiram Eldar_, Dec 20 2022: (Start)
%F a(n) = A084948(n)/2.
%F Sum_{n>=1} 1/a(n) = 2*(e/8^6)^(1/8)*(Gamma(1/4) - Gamma(1/4, 1/8)). (End)
%t 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 *)
%o (PARI) my(x='x+O('x^30)); Vec(serlaplace((-1+(1-8*x)^(-1/4))/2)) \\ _G. C. Greubel_, Feb 26 2018
%o (Magma) [(&*[(8*k-6): k in [1..n]])/2: n in [1..30]]; // _G. C. Greubel_, Feb 26 2018
%Y Cf. A007696, A045755, A034909, A039410, A039411, A039412, A084948.
%K easy,nonn
%O 1,2
%A _Wolfdieter Lang_
%E Terms a(16) onward added by _G. C. Greubel_, Feb 26 2018
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