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 A279663 a(n) = (5/6)^n*Gamma(n+3/5)*Gamma(n+1)*Gamma(n+2)/Gamma(3/5). 1
 1, 1, 8, 208, 12480, 1435200, 281299200, 86640153600, 39507910041600, 25482601976832000, 22424689739612160000, 26147188236387778560000, 39429959860472770068480000, 75350653293363463600865280000, 179334554838205043370059366400000, 523656900127558726640573349888000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Heptagonal pyramidal factorial numbers. LINKS Eric Weisstein's World of Mathematics, Heptagonal Pyramidal Number FORMULA a(n) = Product_{k=1..n} k*(k + 1)*(5*k - 2)/6, a(0)=1. a(n) = Product_{k=1..n} A002413(k), a(0)=1. a(n) ~ (2*Pi)^(3/2)*(5/6)^n*n^(3*n+21/10)/(Gamma(3/5)*exp(3*n)). MATHEMATICA FullSimplify[Table[(5/6)^n Gamma[n + 3/5] Gamma[n + 1] Gamma[n + 2]/Gamma[3/5], {n, 0, 15}]] PROG (MAGMA) [Round((5/6)^n*Gamma(n+3/5)*Gamma(n+1)*Gamma(n+2)/Gamma(3/5)): n in [0..20]]; // Vincenzo Librandi Dec 17 2016 CROSSREFS Cf. A002413. Cf. A084940 (heptagonal factorial numbers). Cf. A087047 (tetrahedral factorial numbers), A135438 (square pyramidal factorial numbers), A167484 (pentagonal pyramidal factorial numbers), A279662 (hexagonal pyramidal factorial numbers). Sequence in context: A063856 A090962 A330287 * A294970 A275286 A255854 Adjacent sequences:  A279660 A279661 A279662 * A279664 A279665 A279666 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Dec 16 2016 STATUS approved

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Last modified January 27 11:44 EST 2021. Contains 340465 sequences. (Running on oeis4.)