|
|
A084942
|
|
Enneagorials: n-th polygorial for k=9.
|
|
19
|
|
|
1, 1, 9, 216, 9936, 745200, 82717200, 12738448800, 2598643555200, 678245967907200, 220429939569840000, 87290256069656640000, 41375581377017247360000, 23128949989752641274240000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = polygorial(n, 9) = (A000142(n)/A000079(n))*A084947(n) = (n!/2^n)*Product_{i=0..n-1} (7*i+2) = (n!/2^n)*7^n*Pochhammer(2/7, n) = (n!/2^n)*7^n*GAMMA(n+2/7)/GAMMA(2/7).
D-finite with recurrence 2*a(n) = n*(7*n-5)*a(n-1). - R. J. Mathar, Mar 12 2019
|
|
MAPLE
|
a := n->n!/2^n*product(7*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[9, #] &, 16, 0] (* Robert G. Wilson v, Dec 26 2016 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003
|
|
STATUS
|
approved
|
|
|
|