A035277 One eighth of deca-factorial numbers.

1, 18, 504, 19152, 919296, 53319168, 3625703424, 282804867072, 24886828302336, 2438909173628928, 263402190751924224, 31081458508727058432, 3978426689117063479296, 549022883098154760142848, 81255386698526904501141504, 12838351098367250911180357632

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..320
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A034301, A045757, A035265, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279.

Programs

GAP

List([1..20], n-> Product([1..n], j-> 10*j-2)/8 ); # G. C. Greubel, Nov 11 2019

Magma

[(&*[10*j-2: j in [1..n]])/8: n in [1..20]]; // G. C. Greubel, Nov 11 2019

Maple

seq( mul(10*j-2, j=1..n)/8, n=1..20); # G. C. Greubel, Nov 11 2019

Mathematica

Table[10^n*Pochhammer[4/5, n]/8, {n,20}] (* G. C. Greubel, Nov 11 2019 *)

PARI

vector(20, n, prod(j=1,n, 10*j-2)/8 ) \\ G. C. Greubel, Nov 11 2019

Sage

[product( (10*j-2) for j in (1..n))/8 for n in (1..20)] # G. C. Greubel, Nov 11 2019

Formula

a(n) = (Pochhammer(8/10,n)*10^n)/8.

8*a(n) = (10*n-2)(!^10) = Product_{j=1..n} (10*j-2).

a(n) = 2^(n+2)*A034301(n) where 4*A034301(n) = (5*n-1)(!^5).

E.g.f.: (-1 + (1-10*x)^(-4/5))/8.

Sum_{n>=1} 1/a(n) = 8*(e/10^2)^(1/10)*(Gamma(4/5) - Gamma(4/5, 1/10)). - Amiram Eldar, Dec 22 2022