OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..220
Daniel Dockery, Polygorials, Special "Factorials" of Polygonal Numbers, preprint, 2003.
FORMULA
a(n) = polygorial(n, 11) = (A000142(n)/A000079(n))*A084949(n) = (n!/2^n)*Product_{i=0..n-1} (9*i+2) = (n!/2^n)*9^n*Pochhammer(2/9, n) = (n!/2^n)*9^n*GAMMA(n+2/9)/GAMMA(2/9).
D-finite with recurrence 2*a(n) = n*(9*n-7)*a(n-1). - R. J. Mathar, Mar 12 2019
MAPLE
a := n->n!/2^n*product(9*i+2, i=0..n-1); [seq(a(j), j=0..30)];
MATHEMATICA
polygorial[k_, n_] := FullSimplify[ n!/2^n (k -2)^n*Pochhammer[2/(k - 2), n]]; Array[polygorial[11, #] &, 16, 0] (* Robert G. Wilson v, Dec 13 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003
STATUS
approved