A369592 Expansion of (1/x) * Series_Reversion( x / (1+x+x^4/(1+x)^3) ).

1, 1, 1, 1, 2, 3, 4, 5, 10, 16, 23, 31, 62, 102, 152, 213, 426, 712, 1084, 1556, 3112, 5255, 8116, 11843, 23686, 40288, 62866, 92842, 185684, 317548, 499376, 744277, 1488554, 2556376, 4044740, 6072124, 12144248, 20926236, 33272912, 50244660, 100489320, 173634752

Offset

0,5

Comments

Number of ordered trees with n+1 edges, having nonroot nodes of outdegree 0 or 4. - Emanuele Munarini, Jun 20 2024

Links

Table of n, a(n) for n=0..41.

Formula

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

Prog

(PARI) my(N=50, x='x+O('x^N)); Vec(serreverse(x/(1+x+x^4/(1+x)^3))/x)
(PARI) a(n) = sum(k=0, n\4, (n-4*k+1)*binomial(n+1, k))/(n+1);

Crossrefs

Cf. A001405, A126042.

Cf. A369525, A369581.

Sequence in context: A134220 A179146 A099161 * A033077 A190912 A306108

Adjacent sequences: A369589 A369590 A369591 * A369593 A369594 A369595

Keyword

nonn

Author

Seiichi Manyama, Jan 26 2024

Status

approved