A366554 G.f. A(x) satisfies A(x) = 1 + x + x^4*A(x)^2.

1, 1, 0, 0, 1, 2, 1, 0, 2, 6, 6, 2, 5, 20, 30, 20, 19, 70, 140, 140, 112, 266, 630, 840, 762, 1176, 2814, 4620, 5049, 6204, 12936, 24156, 31460, 36894, 63492, 123552, 185471, 228800, 338910, 634920, 1050686, 1411410, 1944800, 3354780, 5820256, 8513804, 11644490

Offset

0,6

Links

Table of n, a(n) for n=0..46.

Formula

G.f.: A(x) = 2*(1+x) / (1+sqrt(1-4*x^4*(1+x))).

a(n) = Sum_{k=0..floor(n/4)} binomial(k+1,n-4*k) * binomial(2*k,k)/(k+1).

a(n) = A366589(n) + A366589(n-1).

Prog

(PARI) a(n) = sum(k=0, n\4, binomial(k+1, n-4*k)*binomial(2*k, k)/(k+1));

Crossrefs

Cf. A007477, A025227, A248100.

Cf. A366556, A366558.

Cf. A366589.

Sequence in context: A070677 A269339 A300192 * A029584 A318931 A266878

Adjacent sequences: A366551 A366552 A366553 * A366555 A366556 A366557

Keyword

nonn

Author

Seiichi Manyama, Oct 13 2023

Status

approved