OFFSET
0,2
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+3, 3)/polygorial(3, n+3) = (n+1)!^2*(n+2)*(n+3)*(n+4)/(2^n*24) = A067550(n+2)/2.
a(n) ~ (1/12)*Pi*n^(2*n+6)/(2^n*exp(2*n)). - Ilya Gutkovskiy, Dec 17 2016
D-finite with recurrence 2*a(n) = (n+4)*(n+1)*a(n-1). - R. J. Mathar, Mar 12 2019
MAPLE
a := n->(n+1)!^2*(n+2)*(n+3)*(n+4)/2^n/24; [seq(a(j), j=0..15)];
seq(mul(binomial(k, 2)-binomial(k, 1), k =5..n), n=4..18 ); # Zerinvary Lajos, Aug 07 2007
MATHEMATICA
polygorial[k_, n_] := FullSimplify[ n!/2^n (k -2)^n*Pochhammer[2/(k -2), n]]; Array[ polygorial[3, #]/polygorial[#, 3] &, 17, 3] (* Robert G. Wilson v, Dec 13 2016 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003
STATUS
approved