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

0,3

Comments

Hankel transform is A174811.

Links

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

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A351150 A204326 A151250 * A121545 A078845 A230126

Adjacent sequences: A174807 A174808 A174809 * A174811 A174812 A174813

Keyword

easy,nonn

Author

Paul Barry, Mar 29 2010

Status

approved