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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)), ... 4

%I

%S 1,1,5,70,2100,115500,10510500,1471470000,300179880000,85551265800000,

%T 32937237333000000,16666242090498000000,10833057358823700000000,

%U 8872273976876610300000000,9005358086529759454500000000,11166644027296901723580000000000,16705299464836164978475680000000000,29818959544732554486579088800000000000

%N 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)), ...

%C 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.

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

%C 10^floor(n/3)|a(n). - _G. C. Greubel_, Oct 14 2016

%H G. C. Greubel, <a href="/A135438/b135438.txt">Table of n, a(n) for n = 0..100</a>

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

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

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

%Y Cf. A000330.

%K nonn

%O 0,3

%A _Alexander R. Povolotsky_, Dec 14 2007

%E Edited by _N. J. A. Sloane_, Dec 14 2007

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Last modified October 22 07:06 EDT 2021. Contains 348160 sequences. (Running on oeis4.)