A372016 G.f. A(x) satisfies A(x) = ( 1 + 4*x/(1 - x*A(x)) )^(1/2).

1, 2, 0, 6, -2, 38, -32, 314, -436, 3014, -5732, 31954, -74934, 363642, -983868, 4360230, -13021586, 54374950, -173933428, 698713298, -2345075002, 9189017010, -31903354068, 123070336590, -437701811100, 1672475509274, -6052049207112, 22998585552814

Offset: 0

Author

Seiichi Manyama, Apr 15 2024

Keywords

• sign

Crossrefs

Cf. A372002.

Programs

PARI

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

Formula

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