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A084940 Heptagorials: n-th polygorial for k=7. 21
1, 1, 7, 126, 4284, 235620, 19085220, 2137544640, 316356606720, 59791398670080, 14050978687468800, 4018579904616076800, 1374354327378698265600, 553864793933615401036800, 259762588354865623086259200 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..14.

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

FORMULA

A084940(n) = Polygorial(n, 7) = A000142(n)/A000079(n)*A047055(n) = n!/2^n*product(5*i+2, i=0..n-1) = 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.

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 *)

PROG

(PARI) a(n)=n!/2^n*prod(i=1, n, 5*i-3) \\ Charles R Greathouse IV, Dec 13 2016

CROSSREFS

Cf. A006472, A001044, A000680, A084939, A084941, A084942, A084943, A084944, A085356.

Sequence in context: A295412 A202798 A204248 * A246648 A139987 A061744

Adjacent sequences:  A084937 A084938 A084939 * A084941 A084942 A084943

KEYWORD

easy,nonn

AUTHOR

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

STATUS

approved

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Last modified December 16 01:36 EST 2017. Contains 296063 sequences.