A369581 Expansion of (1/x) * Series_Reversion( x / (1+x+x^4/(1+x)^2) ).

1, 1, 1, 1, 2, 4, 7, 11, 20, 40, 79, 147, 278, 550, 1110, 2204, 4352, 8708, 17689, 35971, 72933, 148271, 303582, 624132, 1283898, 2643354, 5458457, 11306443, 23460067, 48727689, 101363663, 211262307, 441026328, 921743772, 1928573045, 4040272335, 8474803721

Offset

0,5

Links

Table of n, a(n) for n=0..36.

Index entries for reversions of series

Formula

a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+1,k) * binomial(n-3*k+1,n-4*k).

Prog

(PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^4/(1+x)^2))/x)
(PARI) a(n) = sum(k=0, n\4, binomial(n+1, k)*binomial(n-3*k+1, n-4*k))/(n+1);

Crossrefs

Cf. A367414.

Sequence in context: A160393 A018173 A288380 * A146156 A304916 A024927

Adjacent sequences: A369578 A369579 A369580 * A369582 A369583 A369584

Keyword

nonn

Author

Seiichi Manyama, Jan 26 2024

Status

approved