A035275 One sixth of deca-factorial numbers.

1, 16, 416, 14976, 688896, 38578176, 2546159616, 193508130816, 16641699250176, 1597603128016896, 169345931569790976, 19644128062095753216, 2475160135824064905216, 336621778472072827109376, 49146779656922632757968896, 7666897626479930710243147776

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. A034300, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279, A045757.

Programs

GAP

List([1..20], n-> Product([1..n], j-> 10*j-4)/6 ); # G. C. Greubel, Nov 11 2019

Magma

[(&*[10*j-4: j in [1..n]])/6: n in [1..20]]; // G. C. Greubel, Nov 11 2019

Maple

seq( mul(10*j-4, j=1..n)/6, n=1..20); # G. C. Greubel, Nov 11 2019

Mathematica

Table[10^n*Pochhammer[6/10, n]/6, {n, 20}] (* G. C. Greubel, Nov 11 2019 *)

PARI

vector(20, n, prod(j=1,n, 10*j-4)/6 ) \\ G. C. Greubel, Nov 11 2019

Sage

[product( (10*j-4) for j in (1..n))/6 for n in (1..20)] # G. C. Greubel, Nov 11 2019

Formula

6*a(n) = (10*n-4)(!^10) = Product_{j=1..n} (10*j-4).

a(n) = 2^n*3*A034300(n) where 3*A034300(n) = (5*n-2)(!^5).

E.g.f.: (-1 + (1-10*x)^(-3/5))/6.

a(n) = (Pochhammer(6/10,n) * 10^n)/6.

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