A369213 Expansion of (1/x) * Series_Reversion( x / ((1+x)^4+x^2) ).

1, 4, 23, 152, 1091, 8264, 65021, 526236, 4352942, 36637576, 312763225, 2701521420, 23567184019, 207343098824, 1837623853627, 16391011930424, 147029997389386, 1325506554640872, 12003342144724338, 109136630802023808, 995907341988015935

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(4*n-4*k+4,n-2*k).

D-finite with recurrence -3*(4813*n-632)*(3*n+2)*(3*n+4)*(n+1)*a(n) +2*(206141*n^4+1346849*n^3+118471*n^2-121301*n-7584)*a(n-1) +4*(1658281*n^4-3845638*n^3+4346111*n^2-2458136*n+406104)*a(n-2) +8*(n-2)*(2032705*n^3-6230304*n^2+5971619*n-935490)*a(n-3) +16*(n-2)*(n-3)*(958321*n^2-2152552*n+309963)*a(n-4) +544*(8765*n-1142)*(n-2)*(n-3)*(n-4)*a(n-5)=0. - R. J. Mathar, Jan 28 2024

Prog

(PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^4+x^2))/x)
(PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(4*n-4*k+4, n-2*k))/(n+1);

Crossrefs

Cf. A349331, A369126.

Cf. A001006, A065065, A071356.

Sequence in context: A193113 A192730 A246813 * A379088 A055723 A364478

Adjacent sequences: A369210 A369211 A369212 * A369214 A369215 A369216

Keyword

nonn

Author

Seiichi Manyama, Jan 16 2024

Status

approved