A035276 One seventh of deca-factorial numbers.

1, 17, 459, 16983, 798201, 45497457, 3048329619, 234721380663, 20420760117681, 1980813731415057, 211947069261411099, 24797807103585098583, 3149321502155307520041, 431457045795277130245617, 63424185731905738146105699, 9957597159909200888938594743

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. A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279, A045757.

Programs

GAP

List([1..20], n-> Product([1..n], j-> 10*j-3)/7 ); # G. C. Greubel, Nov 11 2019

Magma

[(&*[10*j-3: j in [1..n]])/7: n in [1..20]]; // G. C. Greubel, Nov 11 2019

Maple

seq( mul(10*j-3, j=1..n)/7, n=1..20); # G. C. Greubel, Nov 11 2019

Mathematica

Table[10^n*Pochhammer[7/10, n]/7, {n, 20}] (* G. C. Greubel, Nov 11 2019 *)

PARI

vector(20, n, prod(j=1,n, 10*j-3)/7 ) \\ G. C. Greubel, Nov 11 2019

Sage

[product( (10*j-3) for j in (1..n))/7 for n in (1..20)] # G. C. Greubel, Nov 11 2019

Formula

7*a(n) = (10*n-3)(!^10) = Product_{j=1..n} (10*j-3).

E.g.f.: (-1 + (1-10*x)^(-7/10))/7.

a(n) = (Pochhammer(7/10,n)*10^n)/7.

Sum_{n>=1} 1/a(n) = 7*(e/10^3)^(1/10)*(Gamma(7/10) - Gamma(7/10, 1/10)). - Amiram Eldar, Dec 22 2022