A185089 A transform of the little Schroeder numbers.

1, 1, 2, 3, 7, 14, 35, 81, 208, 517, 1351, 3492, 9261, 24521, 65862, 177247, 481191, 1310338, 3589143, 9862257, 27215012, 75320969, 209147407, 582264200, 1625342649, 4547350865, 12750836298, 35824579355, 100843670951, 284361285238, 803170176715

Offset

0,3

Comments

Hankel transform is A060656.

Links

Fung Lam, Table of n, a(n) for n = 0..2000

Formula

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

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

a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)*A001003(k).

conjecture: (n+2)*a(n) -3*(n+1)*a(n-1) +3*(2-n)*a(n-2) +(11*n-20)*a(n-3) +(11-5*n)*a(n-4) +(4-n)*a(n-5) =0. - R. J. Mathar, Nov 16 2011 (Formula verified and used for computations. - Fung Lam, Feb 24 2014)

Mathematica

CoefficientList[Series[(1-x+x^2-Sqrt[1-2*x-5*x^2+6*x^3+x^4])/(4*x^2*(1-x)), {x, 0, 50}], x] (* G. C. Greubel, Jun 22 2017 *)

Prog

(PARI) x='x+O('x^50); Vec((1-x+x^2-sqrt(1-2*x-5*x^2+6*x^3+x^4))/(4*x^2*(1-x))) \\ G. C. Greubel, Jun 22 2017

Crossrefs

Sequence in context: A328057 A305785 A367387 * A180564 A113822 A036250

Adjacent sequences: A185086 A185087 A185088 * A185090 A185091 A185092

Keyword

nonn,easy

Author

Paul Barry, Feb 18 2011

Status

approved