A034787 a(n) = n-th sextic factorial number divided by 5.

1, 11, 187, 4301, 124729, 4365515, 178986115, 8412347405, 445854412465, 26305410335435, 1709851671803275, 121399468698032525, 9347759089748504425, 775864004449125867275, 69051896395972202187475, 6559930157617359207810125, 662552945919353279988822625

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

D-finite with recurrence: a(n) +(-6*n+1)*a(n-1)=0. - R. J. Mathar, Feb 24 2020

Sum_{n>=1} 1/a(n) = 5*(e/6)^(1/6)*(Gamma(5/6) - Gamma(5/6, 1/6)). - Amiram Eldar, Dec 18 2022

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 *)
With[{nn=20}, CoefficientList[Series[(-1+(1-6x)^(-5/6))/5, {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Dec 21 2024 *)

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

Author

Wolfdieter Lang

Status

approved