A379326 G.f. A(x) satisfies A(x) = sqrt( (1 + 2*x) * (1 + 2*x*A(x)) ).

1, 2, 2, 2, 0, 0, -2, 2, -2, 6, -10, 14, -28, 52, -86, 158, -296, 528, -966, 1806, -3328, 6160, -11542, 21590, -40418, 76118, -143598, 271138, -513524, 974620, -1851962, 3525682, -6723794, 12839190, -24550602, 47010286, -90122848, 172970032, -332352998, 639260230

Offset: 0

Author

Seiichi Manyama, Dec 21 2024

Keywords

• sign

Crossrefs

Cf. A379327, A379328.

Programs

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));

Formula

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

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).