A379209 G.f. A(x) satisfies A(x) = 1/((1 - x*A(x)^2) * (1 - x*A(x))).

1, 2, 9, 53, 357, 2605, 20041, 160074, 1314821, 11036015, 94242752, 816190963, 7151741597, 63287390223, 564791911903, 5077284164245, 45935201005749, 417928249605123, 3821430547469626, 35098466575407095, 323662850948066340, 2995524340795970120

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Stoyan Dimitrov, Nathan Fox, Kimberly Hadaway, Ashley Tharp, and Stephan Wagner, Counting Colored Trees, arXiv:2602.16055 [math.CO], 2026.

Formula

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

a(n) = A190738(n)/(n+1).

Prog

(PARI) a(n) = sum(k=0, n, binomial(n+2*k+1, k)*binomial(2*n, n-k)/(n+2*k+1));

Crossrefs

Cf. A006013, A379189.

Cf. A190738.

Sequence in context: A391083 A074602 A394148 * A192131 A326287 A351815

Adjacent sequences: A379206 A379207 A379208 * A379210 A379211 A379212

Keyword

nonn,changed

Author

Seiichi Manyama, Dec 18 2024

Status

approved