OFFSET
1,2
LINKS
FORMULA
2*a(n) = (6*n-4)(!^6) = Product_{j=1..n} (6*j-4) = 2^n*A007559(n), A007559(n) = (3*n-2)(!^3) = Product_{j=1..n} (3*j-2).
E.g.f.: (-1 + (1-6*x)^(-1/3))/2.
D-finite with recurrence: a(n) = 2*(3*n-2)*a(n-1). - R. J. Mathar, Feb 24 2020
a(n) = 3*6^(n-1)*Pochhammer(n, 1/3). - G. C. Greubel, Oct 21 2022
From Amiram Eldar, Dec 18 2022: (Start)
a(n) = A047657(n)/2.
Sum_{n>=1} 1/a(n) = 2*(e/6^4)^(1/6)*(Gamma(1/3, 1/6) - Gamma(1/3)). (End)
MATHEMATICA
Table[6^n*Pochhammer[1/3, n]/2, {n, 40}] (* G. C. Greubel, Oct 21 2022 *)
PROG
(Magma) [n le 1 select 1 else (6*n-4)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 21 2022
(SageMath) [6^n*rising_factorial(1/3, n)/2 for n in range(1, 40)] # G. C. Greubel, Oct 21 2022
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
STATUS
approved