A157127 A transform of the Catalan numbers with a simple Hankel transform.

1, 0, -1, -1, 1, 2, 1, -3, -5, -1, 11, 15, -5, -44, -41, 51, 169, 85, -303, -611, -15, 1513, 2021, -1271, -6827, -5673, 10361, 28301, 10141, -61102, -107015, 20109, 310387, 356515, -354349, -1421913, -936805, 2567875, 5930631, 972819, -14696329

Offset: 0

Author

Paul Barry, Feb 23 2009

Keywords

• easy
• sign

Comments

Hankel transform is A157128. Partial sums of A157125.

Formula

G.f.: (sqrt(1+x^2+4x^3)-sqrt(1+x^2))/(2*sqrt(1+x^2));

a(n)=sum{k=0..n, A157125(k)};