A369525 Expansion of (1/x) * Series_Reversion( x / (1+x+x^4/(1+x)) ).

1, 1, 1, 1, 2, 5, 11, 21, 40, 84, 190, 429, 944, 2067, 4613, 10505, 24092, 55182, 126444, 291232, 675144, 1571934, 3667774, 8573365, 20090498, 47214710, 111237828, 262587843, 620911708, 1470701157, 3489548683, 8293157045, 19738018740, 47039738570, 112247416400

Offset

0,5

Links

Table of n, a(n) for n=0..34.

Index entries for reversions of series

Formula

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

Prog

(PARI) my(N=40, 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+1, k)*binomial(n-2*k+1, n-4*k))/(n+1);

Crossrefs

Cf. A367317.

Sequence in context: A144700 A000785 A364552 * A364591 A049936 A058358

Adjacent sequences: A369522 A369523 A369524 * A369526 A369527 A369528

Keyword

nonn

Author

Seiichi Manyama, Jan 26 2024

Status

approved