OFFSET
0,3
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
FORMULA
a(n) = (n+1)!*(2*n+1)!/12^n.
MATHEMATICA
Table[(n + 1)! (2 n + 1)!/12^n, {n, 0, 25}] (* G. C. Greubel, Oct 14 2016 *)
PROG
(PARI) a(n) = (n+1)!*(2*n+1)!/12^n
CROSSREFS
KEYWORD
nonn
AUTHOR
Alexander R. Povolotsky, Dec 14 2007
EXTENSIONS
Edited by N. J. A. Sloane, Dec 14 2007
STATUS
approved