A371430 Expansion of (1/x) * Series_Reversion( x / ((1+x)^4 - x^2) ).

1, 4, 21, 128, 851, 5984, 43759, 329396, 2535406, 19863592, 157874971, 1269833668, 10316765299, 84540929568, 697928139977, 5799156785376, 48461097907978, 407020852551016, 3434002483872566, 29090171931564848, 247333930963224287, 2109921586071433064

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Index entries for reversions of series

Formula

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

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, (-1)^k*binomial(n+1, k)*binomial(4*n-4*k+4, n-2*k))/(n+1);

Crossrefs

Cf. A317133, A369156.

Cf. A369213.

Sequence in context: A099250 A293192 A300674 * A232956 A234268 A111177

Adjacent sequences: A371427 A371428 A371429 * A371431 A371432 A371433

Keyword

nonn

Author

Seiichi Manyama, Mar 23 2024

Status

approved