A366591 G.f. A(x) satisfies A(x) = 1 + x^3*(1+x)^2*A(x)^3.

1, 0, 0, 1, 2, 1, 3, 12, 18, 24, 75, 180, 295, 620, 1612, 3365, 6580, 15365, 35728, 74906, 163099, 379242, 848148, 1848693, 4187193, 9583209, 21417924, 48067371, 109877922, 250010451, 564688551, 1286128272, 2944963788, 6714338592, 15313680087, 35108572386

Offset

0,5

Links

Table of n, a(n) for n=0..35.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(2*k,n-3*k) * binomial(3*k,k)/(2*k+1).

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(2*k, n-3*k)*binomial(3*k, k)/(2*k+1));

Crossrefs

Cf. A366221, A366590, A366592.

Cf. A366555.

Sequence in context: A329025 A317548 A320327 * A007447 A153189 A362272

Adjacent sequences: A366588 A366589 A366590 * A366592 A366593 A366594

Keyword

nonn

Author

Seiichi Manyama, Oct 14 2023

Status

approved