OFFSET
0,3
FORMULA
a(n) = [x^n] 1/((1-n*x^3) * (1-x)^n).
a(n) ~ exp(n^(2/3) + n^(1/3)/2 + 1/3) * n^(n/3) / 3. - Vaclav Kotesovec, Apr 08 2024
MATHEMATICA
Join[{1}, Table[Sum[n^k*Binomial[2*n-3*k-1, n-1], {k, 0, n/3}], {n, 1, 25}]] (* Vaclav Kotesovec, Apr 08 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\3, n^k*binomial(2*n-3*k-1, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 08 2024
STATUS
approved