A370836 Expansion of (1/x) * Series_Reversion( x/(x+1/(1+x^2)) ).

1, 1, 0, -2, -2, 6, 19, 1, -98, -170, 268, 1464, 967, -7253, -19035, 11497, 142894, 186814, -592148, -2327480, -371472, 14922592, 30367918, -44517534, -291059645, -242260229, 1550840094, 4611423196, -2050694753, -36095033685, -54276040088, 150373292998

Offset

0,4

Links

Table of n, a(n) for n=0..31.

Index entries for reversions of series

Formula

a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n,2*k) * binomial(3*k,k)/(2*k+1).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x/(x+1/(1+x^2)))/x)
(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(n, 2*k)*binomial(3*k, k)/(2*k+1));

Crossrefs

Cf. A370837, A370838.

Cf. A049130, A370799.

Sequence in context: A365103 A357537 A173098 * A233113 A366731 A341380

Adjacent sequences: A370833 A370834 A370835 * A370837 A370838 A370839

Keyword

sign

Author

Seiichi Manyama, Mar 03 2024

Status

approved