A035272 One third of deca-factorial numbers.

1, 13, 299, 9867, 424281, 22486893, 1416674259, 103417220907, 8583629335281, 798277528181133, 82222585402656699, 9291152150500206987, 1142811714511525459401, 151993958030032886100333, 21735135998294702712347619, 3325475807739089514989185707, 542052556661471590943237270241

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

Programs

GAP

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

Magma

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

Maple

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

Mathematica

Table[10^n*Pochhammer[3/10, n]/3, {n, 20}] (* G. C. Greubel, Nov 11 2019 *)

PARI

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

Sage

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

Formula

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

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

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