OFFSET
0,2
FORMULA
a(n) = [x^n] 1/((1-x-n*x^3) * (1-x)^n).
a(n) ~ exp(4*n^(2/3)/3 + 2*n^(1/3)/9) * n^(n/3) / 3. - Vaclav Kotesovec, Apr 07 2024
MATHEMATICA
Join[{1}, Table[Sum[n^k Binomial[2n-2k, n-3k], {k, 0, Floor[n/3]}], {n, 30}]] (* Harvey P. Dale, Aug 10 2024 *)
PROG
(PARI) a(n) = sum(k=0, n\3, n^k*binomial(2*n-2*k, n-3*k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Apr 07 2024
STATUS
approved