OFFSET
0,3
LINKS
Daniel Dockery, Polygorials, Special "Factorials" of Polygonal Numbers, preprint, 2003.
FORMULA
a(n) = polygorial(n, 7) = (A000142(n)/A000079(n))*A047055(n) = (n!/2^n)*Product_{i=0..n-1}(5*i+2) = (n!/2^n)*5^n*Pochhammer(2/5, n) = (n!/2^n)*5^n*GAMMA(n+2/5)*sin(2*Pi/5)*GAMMA(3/5)/Pi.
D-finite with recurrence 2*a(n) = n*(5*n-3)*a(n-1). - R. J. Mathar, Mar 12 2019
MAPLE
a := n->n!/2^n*mul(5*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[7, #] &, 16, 0] (* Robert G. Wilson v, Dec 26 2016 *)
Join[{1}, FoldList[Times, PolygonalNumber[7, Range[20]]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 29 2019 *)
PROG
(PARI) a(n)=n!/2^n*prod(i=1, n, 5*i-3) \\ Charles R Greathouse IV, Dec 13 2016
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003
STATUS
approved