OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..250
FORMULA
a(n) = Sum_{k=0..n} A132393(n,k)*3^k*9^(n-k).
a(n) = (-6)^n*Sum_{k=0..n} (3/2)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
Sum_{n>=0} 1/a(n) = 1 + (e/9^6)^(1/9)*(Gamma(1/3) - Gamma(1/3, 1/9)). - Amiram Eldar, Dec 21 2022
EXAMPLE
a(0)=1, a(1)=3, a(2)=3*12=36, a(3)=3*12*21=756, a(4)=3*12*21*30=22680, ...
MAPLE
seq(9^n*pochhammer(1/3, n), n = 0..20); # G. C. Greubel, Dec 03 2019
MATHEMATICA
Table[9^n*Pochhammer[1/3, n], {n, 0, 20}] (* G. C. Greubel, Dec 03 2019 *)
PROG
(PARI) a(n)=3^n*prod(i=1, n, 3*i-2) \\ Charles R Greathouse IV, Jan 17 2012
(Magma) [Round(9^n*Gamma(n+1/3)/Gamma(1/3)): n in [0..20]]; // G. C. Greubel, Dec 03 2019
(Sage) [9^n*rising_factorial(1/3, n) for n in (0..20)] # G. C. Greubel, Dec 03 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Sep 20 2008
STATUS
approved