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 *)
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
KEYWORD
easy,nonn
AUTHOR
STATUS
approved