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 A279662 a(n) = (2/3)^n*Gamma(n+3/4)*Gamma(n+1)*Gamma(n+2)/Gamma(3/4). 1
 1, 1, 7, 154, 7700, 731500, 117771500, 29678418000, 11040371496000, 5796195035400000, 4144279450311000000, 3920488359994206000000, 4790836775912919732000000, 7411424492337286825404000000, 14266992147749277138902700000000, 33670101468688294047810372000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Hexagonal pyramidal factorial numbers. More generally, the m-gonal pyramidal factorial numbers is 6^(-n)*(m-2)^n*Gamma(n+1)*Gamma(n+2)*Gamma(n+3/(m-2))/Gamma(3/(m-2)), m>2. LINKS Eric Weisstein's World of Mathematics, Hexagonal Pyramidal Number FORMULA a(n) = Product_{k=1..n} k*(k + 1)*(4*k - 1)/6, a(0)=1. a(n) = Product_{k=1..n} A002412(k), a(0)=1. a(n) ~ (2*Pi)^(3/2)*(2/3)^n*n^(3*n+9/4)/(Gamma(3/4)*exp(3*n)). MATHEMATICA FullSimplify[Table[(2/3)^n Gamma[n + 3/4] Gamma[n + 1] Gamma[n + 2]/Gamma[3/4], {n, 0, 15}]] PROG (MAGMA) [Round((2/3)^n*Gamma(n+3/4)*Gamma(n+1)*Gamma(n+2) / Gamma(3/4)): n in [0..20]]; // Vincenzo Librandi, Dec 17 2016 CROSSREFS Cf. A002412. Cf. A000680 (hexagonal factorial numbers). Cf. A087047 (tetrahedral factorial numbers), A135438 (square pyramidal factorial numbers), A167484 (pentagonal pyramidal factorial numbers), A279663 (heptagonal pyramidal factorial numbers). Sequence in context: A144683 A229711 A296232 * A214382 A141835 A111831 Adjacent sequences:  A279659 A279660 A279661 * A279663 A279664 A279665 KEYWORD nonn AUTHOR Ilya Gutkovskiy, Dec 16 2016 STATUS approved

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Last modified January 25 14:42 EST 2021. Contains 340416 sequences. (Running on oeis4.)