OFFSET
0,2
FORMULA
a(n) ~ c * 3^(3*n + 1/2) / (sqrt(Pi*n) * 2^(2*n + 1)), where c = Sum_{j>=0} p(j)/2^j = A065446 = 3.4627466194550636115379573429...
MATHEMATICA
Table[Sum[PartitionsP[k]*Binomial[3*n, n-k], {k, 0, n}], {n, 0, 30}]
PROG
(PARI) a(n) = sum(k=0, n, binomial(3*n, n-k)*numbpart(k)); \\ Michel Marcus, Aug 02 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Aug 01 2022
STATUS
approved