A366646 G.f. A(x) satisfies A(x) = 1 + (x * A(x) / (1 - x))^4.

1, 0, 0, 0, 1, 4, 10, 20, 39, 88, 228, 600, 1507, 3652, 8866, 22100, 56365, 144656, 369784, 942480, 2408934, 6196280, 16026652, 41571640, 107959654, 280708560, 731349400, 1910098320, 4999759830, 13109582376, 34421585844, 90500370760, 238272324682

Offset

0,6

Links

Table of n, a(n) for n=0..32.

Formula

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

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(n-1, n-4*k)*binomial(4*k, k)/(3*k+1));

Crossrefs

Partial sums give A127902.

Cf. A213336, A364410, A366645.

Cf. A002026, A361932.

Sequence in context: A128640 A128641 A164617 * A038421 A049032 A100354

Adjacent sequences: A366643 A366644 A366645 * A366647 A366648 A366649

Keyword

nonn

Author

Seiichi Manyama, Oct 15 2023

Status

approved