%I #20 Dec 22 2022 08:29:16
%S 1,16,416,14976,688896,38578176,2546159616,193508130816,
%T 16641699250176,1597603128016896,169345931569790976,
%U 19644128062095753216,2475160135824064905216,336621778472072827109376,49146779656922632757968896,7666897626479930710243147776
%N One sixth of deca-factorial numbers.
%H G. C. Greubel, <a href="/A035275/b035275.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 6*a(n) = (10*n-4)(!^10) = Product_{j=1..n} (10*j-4).
%F a(n) = 2^n*3*A034300(n) where 3*A034300(n) = (5*n-2)(!^5).
%F E.g.f.: (-1 + (1-10*x)^(-3/5))/6.
%F a(n) = (Pochhammer(6/10,n) * 10^n)/6.
%F Sum_{n>=1} 1/a(n) = 6*(e/10^4)^(1/10)*(Gamma(3/5) - Gamma(3/5, 1/10)). - _Amiram Eldar_, Dec 22 2022
%p seq( mul(10*j-4, j=1..n)/6, n=1..20); # _G. C. Greubel_, Nov 11 2019
%t Table[10^n*Pochhammer[6/10, n]/6, {n, 20}] (* _G. C. Greubel_, Nov 11 2019 *)
%o (PARI) vector(20, n, prod(j=1,n, 10*j-4)/6 ) \\ _G. C. Greubel_, Nov 11 2019
%o (Magma) [(&*[10*j-4: j in [1..n]])/6: n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o (Sage) [product( (10*j-4) for j in (1..n))/6 for n in (1..20)] # _G. C. Greubel_, Nov 11 2019
%o (GAP) List([1..20], n-> Product([1..n], j-> 10*j-4)/6 ); # _G. C. Greubel_, Nov 11 2019
%Y Cf. A034300, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279, A045757.
%K easy,nonn
%O 1,2
%A _Wolfdieter Lang_