OFFSET
1,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..150
FORMULA
a(n) = Sum_{k=0..n} (-1)^k (3n-k)!/(6^(n-k)*2^k) * binomial(n,k).
a(n) ~ sqrt(Pi) * 3^(2*n + 1/2) * n^(3*n + 1/2) / (2^(n - 1/2) * exp(3*n+1)). - Vaclav Kotesovec, Oct 21 2023
MATHEMATICA
a[n_]:= a[n]= Sum[(-1)^j*Binomial[n, j]*(3*n-j)!/(2^j*6^(n-j)), {j, 0, n}];
Table[a[n], {n, 30}] (* G. C. Greubel, Jul 13 2021 *)
Table[(3*n)! * Hypergeometric1F1[-n, -3*n, -3] / 6^n, {n, 1, 20}] (* Vaclav Kotesovec, Oct 21 2023 *)
PROG
(PARI) a(n)= sum(k=0, n, (-1)^k *(3*n-k)! /(6^(n-k)*2^k) * binomial(n, k)) \\ Michel Marcus, Jul 25 2013
(Sage)
def A173789(n): return sum( (-1)^j*binomial(n, j)*factorial(3*n-j)/(2^j*6^(n-j)) for j in (0..n))
[A173789(n) for n in (1..30)] # G. C. Greubel, Jul 13 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Shanzhen Gao, Feb 24 2010
STATUS
approved