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A034723 a(n) = n-th sextic factorial number divided by 3. 8
1, 9, 135, 2835, 76545, 2525985, 98513415, 4433103675, 226088287425, 12887032383225, 811883040143175, 56019929769879075, 4201494732740930625, 340321073352015380625, 29607933381625338114375 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

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

FORMULA

3*a(n) = (6*n-3)(!^6) = Product_{j=1..n} (6*j-3) = 3^n*A001147(n) = 3^n*(2*n)!/(2^n*n!).

E.g.f.: (-1 + (1-6*x)^(-1/2))/3.

a(n) = 2*(3/2)^(n-1)*(n+1)!*C(n), where C(n) = A000108(n). - G. C. Greubel, Nov 11 2019

D-finite with recurrence: a(n) +3*(-2*n+1)*a(n-1)=0. - R. J. Mathar, Feb 24 2020

MAPLE

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

MATHEMATICA

Table[3^(n-1)*(2*n)!/(2^n*n!), {n, 20}] (* G. C. Greubel, Nov 11 2019 *)

PROG

(PARI) a(n) = prod(j=1, n, 6*j-3)/3; \\ Michel Marcus, Mar 13 2019

(MAGMA) F:=Factorial; [3^(n-1)*F(2*n)/(2^n*F(n)): n in [1..20]]; // G. C. Greubel, Nov 11 2019

(Sage) f=factorial; [3^(n-1)*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^(n-1)*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

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Last modified April 15 01:24 EDT 2021. Contains 342974 sequences. (Running on oeis4.)