A369226 Expansion of (1/x) * Series_Reversion( x * (1-x) / (1+x^2)^2 ).

1, 1, 4, 13, 53, 220, 968, 4373, 20271, 95705, 458904, 2228220, 10934524, 54143848, 270189008, 1357428997, 6860264323, 34853234867, 177900211204, 911867479717, 4691701977973, 24222505191984, 125448280976224, 651555603531308, 3392951906596708, 17711433386188300

Offset

0,3

Links

Table of n, a(n) for n=0..25.

Peter Bala, Fractional iteration of a series inversion operator

Index entries for reversions of series

Formula

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

a(n) = (1/(n+1)) * [x^n] ( 1/(1-x) * (1+x^2)^2 )^(n+1). - Seiichi Manyama, Feb 14 2024

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)/(1+x^2)^2)/x)
(PARI) a(n, s=2, t=2, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((u+1)*(n+1)-s*k-2, n-s*k))/(n+1);

Crossrefs

Cf. A052709, A369262.

Cf. A218045, A370243.

Sequence in context: A140454 A149465 A149466 * A006604 A082570 A145208

Adjacent sequences: A369223 A369224 A369225 * A369227 A369228 A369229

Keyword

nonn

Author

Seiichi Manyama, Jan 18 2024

Status

approved