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A034787 a(n) = n-th sextic factorial number divided by 5. 10
1, 11, 187, 4301, 124729, 4365515, 178986115, 8412347405, 445854412465, 26305410335435, 1709851671803275, 121399468698032525, 9347759089748504425, 775864004449125867275, 69051896395972202187475 (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

5*a(n) = (6*n-1)(!^6) = Product_{j=1..n} (6*j-1) = (6*n)!/(3^(2*n)*2^(2*n+1)*(2*n)!*A008542(n)*A007559(n)*A034000(n)).

E.g.f.: (-1 + (1-6*x)^(-5/6))/5.

a(n) ~ sqrt(2*Pi) * 6/(5*Gamma(5/6)) * n^(4/3) * (6*n/e)^n * (1 + (61/72)/n + ...}. - Joe Keane (jgk(AT)jgk.org), Nov 24 2001

MAPLE

seq( mul(6*j-1, j=1..n)/5, n=1..20); # G. C. Greubel, Nov 11 2019

MATHEMATICA

Table[6^n*Pochhammer[5/6, n]/5, {n, 20}] (* G. C. Greubel, Nov 11 2019 *)

PROG

(PARI) vector(20, n, prod(j=1, n, 6*j-1)/5 ) \\ G. C. Greubel, Nov 11 2019

(MAGMA) [(&*[6*j-1: j in [1..n]])/5: n in [1..20]]; // G. C. Greubel, Nov 11 2019

(Sage) [product( (6*j-1) for j in (1..n))/5 for n in (1..20)] # G. C. Greubel, Nov 11 2019

(GAP) List([1..20], n-> Product([1..n], j-> 6*j-1)/5 ); # G. C. Greubel, Nov 11 2019

CROSSREFS

Cf. A008542, A034689, A034723, A034724, A034788.

Sequence in context: A209351 A287062 A215203 * A001408 A298643 A185123

Adjacent sequences:  A034784 A034785 A034786 * A034788 A034789 A034790

KEYWORD

easy,nonn,changed

AUTHOR

Wolfdieter Lang

STATUS

approved

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Last modified November 19 16:37 EST 2019. Contains 329323 sequences. (Running on oeis4.)