A360812 Expansion of Sum_{k>=0} ( x / (1 - (k * x)^2) )^k.

1, 1, 1, 2, 9, 29, 113, 613, 3033, 17010, 110929, 713249, 5061097, 38762873, 302389553, 2544613578, 22404995001, 203762678941, 1960880744337, 19509713674397, 201306862742217, 2166901479447194, 24018963506471921, 275731857268608673, 3271769647891351705

Offset

0,4

Links

Table of n, a(n) for n=0..24.

Formula

a(n) = Sum_{k=0..floor(n/2)} (n-2*k)^(2*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)^(2*k)*binomial(n-k-1, k));

Crossrefs

Cf. A339481, A360787.

Sequence in context: A241774 A183383 A280853 * A268568 A150902 A150903

Adjacent sequences: A360809 A360810 A360811 * A360813 A360814 A360815

Keyword

nonn

Author

Seiichi Manyama, Feb 21 2023

Status

approved