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A084944
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Hendecagorials: n-th polygorial for k=11.
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20
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1, 1, 11, 330, 19140, 1818300, 256380300, 50250538800, 13065140088000, 4350691649304000, 1805537034461160000, 913601739437346960000, 553642654099032257760000, 395854497680808064298400000
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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, 11) = (A000142(n)/A000079(n))*A084949(n) = (n!/2^n)*Product_{i=0..n-1} (9*i+2) = (n!/2^n)*9^n*Pochhammer(2/9, n) = (n!/2^n)*9^n*GAMMA(n+2/9)/GAMMA(2/9).
D-finite with recurrence 2*a(n) = n*(9*n-7)*a(n-1). - R. J. Mathar, Mar 12 2019
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MAPLE
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a := n->n!/2^n*product(9*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[11, #] &, 16, 0] (* Robert G. Wilson v, Dec 13 2016 *)
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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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