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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

Table of n, a(n) for n=0..13.

Daniel Dockery, Polygorials, Special "Factorials" of Polygonal Numbers.

FORMULA

a(n) = Polygorial(n, 9) = A000142(n)/A000079(n)*A084947(n) = n!/2^n*product(7*i+2, i=0..n-1) = n!/2^n*7^n*pochhammer(2/7, n) = n!/2^n*7^n*GAMMA(n+2/7)/GAMMA(2/7).

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

(PARI) a(n)=n!/2^n*prod(i=1, n, 7*i-5) \\ Charles R Greathouse IV, Dec 13 2016

CROSSREFS

Cf. A006472, A001044, A000680, A084939, A084940, A084941, A084943, A084944, A085356.

Sequence in context: A007107 A217042 A064633 * A061718 A085741 A211044

Adjacent sequences:  A084939 A084940 A084941 * A084943 A084944 A084945

KEYWORD

easy,nonn

AUTHOR

Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003

STATUS

approved

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Last modified February 19 20:48 EST 2018. Contains 299357 sequences. (Running on oeis4.)