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A360811
Expansion of Sum_{k>=0} ( x / (1 - k * x^3) )^k.
2
1, 1, 1, 1, 2, 5, 10, 18, 38, 91, 211, 472, 1108, 2754, 6881, 17101, 43443, 113565, 300142, 797191, 2147414, 5883976, 16293712, 45471429, 128285353, 366266188, 1055534118, 3066483484, 8989837397, 26602652605, 79370560477, 238606427241, 722973445270
OFFSET
0,5
LINKS
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
Sequence in context: A327064 A246840 A301885 * A127297 A018739 A325648
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 21 2023
STATUS
approved