A279663 a(n) = (5/6)^n*Gamma(n+3/5)*Gamma(n+1)*Gamma(n+2)/Gamma(3/5).

1, 1, 8, 208, 12480, 1435200, 281299200, 86640153600, 39507910041600, 25482601976832000, 22424689739612160000, 26147188236387778560000, 39429959860472770068480000, 75350653293363463600865280000, 179334554838205043370059366400000, 523656900127558726640573349888000000

Offset

0,3

Comments

Heptagonal pyramidal factorial numbers.

Links

Table of n, a(n) for n=0..15.

Eric Weisstein's World of Mathematics, Heptagonal Pyramidal Number

Index to sequences related to pyramidal numbers

Index entries for sequences related to factorial numbers

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: A359452 A394680 A330287 * A294970 A275286 A255854

Adjacent sequences: A279660 A279661 A279662 * A279664 A279665 A279666

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 16 2016

Status

approved