OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..166
FORMULA
a(n) ~ sqrt(Pi) * 3^(2*n + 1/2) * n^(3*n + 1/2) / (2^(n - 1/2) * exp(3*n - 1)). - Vaclav Kotesovec, May 24 2020
EXAMPLE
a(2) = binomial(0+0,0) + binomial(0+1,1) + binomial(0+2,2) + binomial(0+3,3) + binomial(1+0,0) + binomial(1+1,1) + binomial(1+2,2) + binomial(1+3,3) + binomial(2+0,0) + binomial(2+1,1) + binomial(2+2,2) + binomial(2+3,3) + binomial(3+0,0) + binomial(3+1,1) + binomial(3+2,2) + binomial(3+3,3) = 69.
MATHEMATICA
Table[Total[CoefficientList[Series[(1 + x + x^2/2 + x^3/6)^n, {x, 0, 3*n}], x]*Range[0, 3*n]!], {n, 0, 15}] (* Vaclav Kotesovec, May 24 2020 *)
PROG
(PARI) {a(n) = sum(i=0, 3*n, i!*polcoef(sum(j=0, 3, x^j/j!)^n, i))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 19 2019
STATUS
approved