A174810 A transform of the little Schroeder numbers A001003.

1, 1, 4, 17, 81, 410, 2169, 11847, 66306, 378297, 2192011, 12864668, 76313865, 456837181, 2756271064, 16743326577, 102319639173, 628599899558, 3880049052441, 24051163355499, 149654739889478, 934426798835377

Offset: 0

Author

Paul Barry, Mar 29 2010

Keywords

• easy
• nonn

Comments

Hankel transform is A174811.

Links

• Fung Lam, Table of n, a(n) for n = 0..1000

Programs

Mathematica

CoefficientList[Series[(1+x+x^2-Sqrt[1-6*x-5*x^2+2*x^3+x^4])/(4*x*(1+x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Jan 30 2014 *)

PARI

x='x+O('x^66); Vec((1+x+x^2-sqrt(1-6*x-5*x^2+2*x^3+x^4))/(4*x*(1+x))) \\ Joerg Arndt, Jan 30 2014

Formula

G.f.: (1+x+x^2-sqrt(1-6x-5x^2+2x^3+x^4))/(4x(1+x));

G.f.: 1/(1-x(1+x)/(1-2x(1+x)/(1-x(1+x)/(1-2x(1+x)/(1-... (continued fraction);

a(n)=sum{k=0..n, C(k,n-k)*A001003(k)}.

Recurrence: (n+1)*a(n) = (5-n)*a(n-5) - 3*(n-4)*a(n-4) + 3*(n-1)*a(n-3) + (11*n-13)*a(n-2) + (5*n-4)*a(n-1). - Fung Lam, Jan 30 2014