%I #18 Dec 22 2022 08:40:19

%S 1,15,375,13125,590625,32484375,2111484375,158361328125,

%T 13460712890625,1278767724609375,134270611083984375,

%U 15441120274658203125,1930140034332275390625,260568904634857177734375,37782491172054290771484375,5856286131668415069580078125

%N One fifth of deca-factorial numbers.

%C a(n)= (Pochhammer(5/10,n)*10^n)/5.

%H G. C. Greubel, <a href="/A035274/b035274.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 5*a(n) = (10*n-5)(!^10) = Product_{j=1..n} (10*j-5).

%F a(n) = 5^n*A001147(n) where A001147(n) = (2*n-1)!!.

%F E.g.f.: (-1 + (1-10*x)^(-1/2))/5.

%F a(n) = (Pochhammer(5/10,n)*10^n)/5.

%F Sum_{n>=1} 1/a(n) = exp(1/10)*sqrt(5*Pi/2)*erf(1/sqrt(10)), where erf is the error function. - _Amiram Eldar_, Dec 22 2022

%p seq( mul(10*j-5, j=1..n)/5, n=1..20); # _G. C. Greubel_, Nov 11 2019

%t Table[10^n*Pochhammer[5/10, n]/5, {n,20}] (* _G. C. Greubel_, Nov 11 2019 *)

%o (PARI) vector(20, n, prod(j=1,n, 10*j-5)/5 ) \\ _G. C. Greubel_, Nov 11 2019

%o (Magma) [(&*[10*j-5: j in [1..n]])/5: n in [1..20]]; // _G. C. Greubel_, Nov 11 2019

%o (Sage) [product( (10*j-5) for j in (1..n))/5 for n in (1..20)] # _G. C. Greubel_, Nov 11 2019

%o (GAP) List([1..20], n-> Product([1..n], j-> 10*j-5)/5 ); # _G. C. Greubel_, Nov 11 2019

%Y Cf. A001147, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279, A045757.

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_