A369503 Expansion of (1/x) * Series_Reversion( x / ((1+x)^2+x^2)^2 ).

1, 4, 24, 168, 1284, 10384, 87360, 756704, 6703168, 60444928, 552990592, 5120101760, 47887472000, 451759449600, 4293634467840, 41073654689280, 395170166443008, 3821262491103232, 37118973530660864, 362035991963869184, 3544080121528001536

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(2*n+2,k) * binomial(4*n-2*k+4,n-2*k).

Prog

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

Crossrefs

Cf. A369502, A369504.

Sequence in context: A339346 A214377 A331007 * A212277 A246423 A188913

Adjacent sequences: A369500 A369501 A369502 * A369504 A369505 A369506

Keyword

nonn

Author

Seiichi Manyama, Jan 25 2024

Status

approved