%I #19 Dec 22 2022 06:33:54
%S 1,12,264,8448,354816,18450432,1143926784,82362728448,6753743732736,
%T 621344423411712,63377131187994624,7098238693055397888,
%U 865985120552758542336,114310035912964127588352,16232025099640906117545984,2467267815145417729866989568,399697386053557672238452310016
%N One half of deca-factorial numbers.
%H G. C. Greubel, <a href="/A035265/b035265.txt">Table of n, a(n) for n = 1..320</a>
%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F 2*a(n) = (10*n-8)(!^10) = Product_{j=1..n} (10*j-8).
%F a(n) = 2^n*A008548(n) where A008548(n) = (5*n-4)(!^5) = Product_{j=1..n} (5*j-4).
%F E.g.f.: (-1 + (1-10*x)^(-1/5))/2.
%F a(n) = (Pochhammer(2/10,n)*10^n)/2.
%F Sum_{n>=1} 1/a(n) = 2*(e/10^8)^(1/10)*(Gamma(1/5) - Gamma(1/5, 1/10)). - _Amiram Eldar_, Dec 22 2022
%p seq( mul(10*j-8, j=1..n)/2, n=1..20); # _G. C. Greubel_, Nov 11 2019
%t Table[10^n*Pochhammer[2/10, n]/2, {n,20}] (* _G. C. Greubel_, Nov 11 2019 *)
%o (PARI) vector(20, n, prod(j=1,n, 10*j-8)/2 ) \\ _G. C. Greubel_, Nov 11 2019
%o (Magma) [(&*[10*j-8: j in [1..n]])/2: n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o (Sage) [product( (10*j-8) for j in (1..n))/2 for n in (1..20)] # _G. C. Greubel_, Nov 11 2019
%o (GAP) List([1..20], n-> Product([1..n], j-> 10*j-8)/2 ); # _G. C. Greubel_, Nov 11 2019
%Y Cf. A008548, A045757, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279.
%K easy,nonn
%O 1,2
%A _Wolfdieter Lang_