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A360810
Expansion of Sum_{k>=0} ( x / (1 - k * x^2) )^k.
1
1, 1, 1, 2, 5, 11, 29, 81, 229, 696, 2181, 7045, 23653, 81433, 288173, 1046814, 3887749, 14768783, 57275541, 226462801, 912443397, 3741515804, 15603500797, 66134448329, 284660214181, 1243605590897, 5511058189989, 24760003963802, 112726590916645
OFFSET
0,4
FORMULA
a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^k * binomial(n-k-1,k).
PROG
(PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, (x/(1-k*x^2))^k))
(PARI) a(n) = sum(k=0, n\2, (n-2*k)^k*binomial(n-k-1, k));
CROSSREFS
Sequence in context: A316769 A192785 A334578 * A320171 A014211 A160911
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 21 2023
STATUS
approved