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A084943
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Decagorials: n-th polygorial for k=10.
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19
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1, 1, 10, 270, 14040, 1193400, 150368400, 26314470000, 6104957040000, 1813172240880000, 670873729125600000, 302564051835645600000, 163384587991248624000000, 104075982550425373488000000
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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, 10) = (A000142(n)/A000079(n))*A084948(n) = (n!/2^n)*Product_{i=0..n-1} (8*i+2) = (n!/2^n)*8^n*Pochhammer(1/4, n) = (n!/2)*4^n*GAMMA(n+1/4)*sqrt(2)*GAMMA(3/4)/Pi.
a(n) = Product_{k=1..n} k*(4k-3). - Daniel Suteu, Nov 01 2017
D-finite with recurrence a(n) -n*(4*n-3)*a(n-1)=0. - R. J. Mathar, May 02 2022
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MAPLE
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a := n->n!/2^n*product(8*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[10, #] &, 14, 0] (* Robert G. Wilson v, Dec 26 2016 *)
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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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