

A034723


a(n) = nth sextic factorial number divided by 3.


8



1, 9, 135, 2835, 76545, 2525985, 98513415, 4433103675, 226088287425, 12887032383225, 811883040143175, 56019929769879075, 4201494732740930625, 340321073352015380625, 29607933381625338114375
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OFFSET

1,2


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..345


FORMULA

3*a(n) = (6*n3)(!^6) = Product_{j=1..n} (6*j3) = 3^n*A001147(n) = 3^n*(2*n)!/(2^n*n!).
E.g.f.: (1 + (16*x)^(1/2))/3.
a(n) = 2*(3/2)^(n1)*(n+1)!*C(n), where C(n) = A000108(n).  G. C. Greubel, Nov 11 2019


MAPLE

seq(3^(n1)*(2*n)!/(2^n*n!), n=1..20); # G. C. Greubel, Nov 11 2019


MATHEMATICA

Table[3^(n1)*(2*n)!/(2^n*n!), {n, 20}] (* G. C. Greubel, Nov 11 2019 *)


PROG

(PARI) a(n) = prod(j=1, n, 6*j3)/3; \\ Michel Marcus, Mar 13 2019
(MAGMA) F:=Factorial; [3^(n1)*F(2*n)/(2^n*F(n)): n in [1..20]]; // G. C. Greubel, Nov 11 2019
(Sage) f=factorial; [3^(n1)*f(2*n)/(2^n*f(n)) for n in (1..20)] # G. C. Greubel, Nov 11 2019
(GAP) F:=Factorial;; List([1..20], n> 3^(n1)*F(2*n)/(2^n*F(n))); # G. C. Greubel, Nov 11 2019


CROSSREFS

Cf. A001147, A008542, A034689.
Sequence in context: A254282 A235339 A306848 * A188685 A052137 A003376
Adjacent sequences: A034720 A034721 A034722 * A034724 A034725 A034726


KEYWORD

easy,nonn


AUTHOR

Wolfdieter Lang


STATUS

approved



