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 A084941 Octagorials: n-th polygorial for k=8. 19
 1, 1, 8, 168, 6720, 436800, 41932800, 5577062400, 981562982400, 220851671040000, 61838467891200000, 21086917550899200000, 8603462360766873600000, 4138265395528866201600000, 2317428621496165072896000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Daniel Dockery, Polygorials, Special "Factorials" of Polygonal Numbers, preprint, 2003. FORMULA a(n) = polygorial(n, 8) = (A000142(n)/A000079(n))*A047657(n) = (n!/2^n)*Product_{i=0..n-1} (6*i+2) = (n!/2^n)*6^n*Pochhammer(1/3, n) = (n!/2)*3^n*sqrt(3)*GAMMA(n+1/3)*GAMMA(2/3)/Pi. a(n) = n*(3*n-2)*a(n-1). - R. J. Mathar, Mar 12 2019 MAPLE a := n->n!/2^n*product(6*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[8, #] &, 16, 0] (* Robert G. Wilson v, Dec 26 2016 *) PROG (PARI) a(n) = n! / 2^n * prod(i=0, n-1, 6*i+2) \\ Felix FrÃ¶hlich, Dec 13 2016 CROSSREFS Cf. A006472, A001044, A000680, A084939, A084940, A084942, A084943, A084944, A085356. Sequence in context: A253974 A254459 A254129 * A139564 A264113 A181198 Adjacent sequences:  A084938 A084939 A084940 * A084942 A084943 A084944 KEYWORD easy,nonn AUTHOR Daniel Dockery (peritus(AT)gmail.com), Jun 13 2003 STATUS approved

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Last modified October 21 06:58 EDT 2019. Contains 328292 sequences. (Running on oeis4.)