A035274 One fifth of deca-factorial numbers.

1, 15, 375, 13125, 590625, 32484375, 2111484375, 158361328125, 13460712890625, 1278767724609375, 134270611083984375, 15441120274658203125, 1930140034332275390625, 260568904634857177734375, 37782491172054290771484375, 5856286131668415069580078125

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Comments

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

Links

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

Crossrefs

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

Programs

GAP

List([1..20], n-> Product([1..n], j-> 10*j-5)/5 ); # G. C. Greubel, Nov 11 2019

Magma

[(&*[10*j-5: j in [1..n]])/5: n in [1..20]]; // G. C. Greubel, Nov 11 2019

Maple

seq( mul(10*j-5, j=1..n)/5, n=1..20); # G. C. Greubel, Nov 11 2019

Mathematica

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

PARI

vector(20, n, prod(j=1,n, 10*j-5)/5 ) \\ G. C. Greubel, Nov 11 2019

Sage

[product( (10*j-5) for j in (1..n))/5 for n in (1..20)] # G. C. Greubel, Nov 11 2019

Formula

5*a(n) = (10*n-5)(!^10) = Product_{j=1..n} (10*j-5).

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

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

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

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