A369208 Expansion of (1/x) * Series_Reversion( x * (1-x)^2 / (1+x^2) ).

1, 2, 8, 38, 200, 1122, 6576, 39790, 246672, 1558658, 10001592, 64997814, 426922392, 2829624514, 18901301984, 127115260894, 859978039840, 5848754717314, 39964745880552, 274231943135686, 1888891689752680, 13055393137141282, 90517646431869328

Offset

0,2

Links

Table of n, a(n) for n=0..22.

P. 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(n+1,k) * binomial(3*n-2*k+1,n-2*k).

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

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2/(1+x^2))/x)
(PARI) a(n, s=2, t=1, u=2) = 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. A218045, A369263.

Cf. A052709, A109081.

Cf. A370242.

Sequence in context: A364723 A372107 A266797 * A234939 A365751 A192784

Adjacent sequences: A369205 A369206 A369207 * A369209 A369210 A369211

Keyword

nonn

Author

Seiichi Manyama, Jan 18 2024

Status

approved