A379327 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x*A(x)^2) * (1 + 2*x*A(x)) ).

1, 2, 6, 22, 88, 372, 1634, 7382, 34078, 160034, 762078, 3671178, 17858476, 87599696, 432804190, 2151867226, 10758455224, 54053627604, 272780539742, 1382047628514, 7027307040920, 35848334763884, 183417043984246, 941007480667474, 4839875674661214, 24950493967407850

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

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

Prog

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

Crossrefs

Cf. A379326, A379328.

Cf. A007863, A379279.

Sequence in context: A333080 A096267 A150264 * A294593 A214358 A107944

Adjacent sequences: A379324 A379325 A379326 * A379328 A379329 A379330

Keyword

nonn

Author

Seiichi Manyama, Dec 21 2024

Status

approved