A135438 Denominators (numerators are all 1) of the series: 1/1^2, (1/1^2)*(1/(1^2+2^2)), (1/1^2)*(1/(1^2+2^2))*(1/(1^2+2^2+3^2)), ...

1, 1, 5, 70, 2100, 115500, 10510500, 1471470000, 300179880000, 85551265800000, 32937237333000000, 16666242090498000000, 10833057358823700000000, 8872273976876610300000000, 9005358086529759454500000000, 11166644027296901723580000000000, 16705299464836164978475680000000000, 29818959544732554486579088800000000000

Offset: 0

Author

Alexander R. Povolotsky, Dec 14 2007

Keywords

• nonn

Comments

The series converges to hypergeom([1], [2, 5/2, 3], 3). The sum is the Engels expansions of the limit. The n-th fraction is 12^n / ( (n+1)! (2n+1)! ). The denominators are given by (n+1)!*(2*n+1)!/12^n.

Terms of this sequence for n>= 1 are products of factors of consecutive terms of A000330.

10^floor(n/3)|a(n). - G. C. Greubel, Oct 14 2016

Links

• G. C. Greubel, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A000330.

Programs

Mathematica

Table[(n + 1)! (2 n + 1)!/12^n, {n, 0, 25}] (* G. C. Greubel, Oct 14 2016 *)

PARI

a(n) = (n+1)!*(2*n+1)!/12^n

Formula

a(n) = (n+1)!*(2*n+1)!/12^n.

Extensions

Edited by N. J. A. Sloane, Dec 14 2007