A367317 Expansion of (1/x) * Series_Reversion( x * (1-x-x^4/(1-x)) ).

1, 1, 2, 5, 15, 50, 177, 649, 2436, 9307, 36080, 141610, 561732, 2248709, 9073415, 36863549, 150676275, 619169360, 2556446520, 10600160707, 44121921044, 184291848864, 772204252280, 3244999395406, 13672564904027, 57749354647408, 244469827514066

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Index entries for reversions of series

Formula

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

Prog

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

Crossrefs

Cf. A001003, A054515.

Cf. A063021, A367414, A367415.

Sequence in context: A370801 A024718 A149951 * A157135 A196836 A365247

Adjacent sequences: A367314 A367315 A367316 * A367318 A367319 A367320

Keyword

nonn

Author

Seiichi Manyama, Jan 26 2024

Status

approved