OFFSET
0,5
LINKS
Robert Israel, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = Sum_{k=0..floor(n/3)} (n-3*k)^k * binomial(n-2*k-1,k).
MAPLE
N:= 100:
F:= 1 + add((x/(1-k*x^3))^k, k=1..N):
S:= series(F, x, N+1):
seq(coeff(S, x, k), k=0..N); # Robert Israel, Feb 21 2024
PROG
(PARI) my(N=40, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k*x^3))^k))
(PARI) a(n) = sum(k=0, n\3, (n-3*k)^k*binomial(n-2*k-1, k));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 21 2023
STATUS
approved