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A084940
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Heptagorials: n-th polygorial for k=7.
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20
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1, 1, 7, 126, 4284, 235620, 19085220, 2137544640, 316356606720, 59791398670080, 14050978687468800, 4018579904616076800, 1374354327378698265600, 553864793933615401036800, 259762588354865623086259200
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OFFSET
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0,3
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LINKS
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FORMULA
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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
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MAPLE
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a := n->n!/2^n*mul(5*i+2, i=0..n-1); [seq(a(j), j=0..30)];
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MATHEMATICA
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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 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003
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STATUS
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approved
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