A166694 A transform of the large Schroeder numbers, A006318.

1, 2, 10, 52, 290, 1706, 10440, 65822, 424710, 2791340, 18622510, 125791894, 858621680, 5913143706, 41036613570, 286702877908, 2014876764170, 14234073943986, 101025202379480, 720017430722598, 5151008515543790

Offset

0,2

Comments

Apply the Riordan array (1,x/(1-x)^2) to the large Schroeder numbers.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Formula

G.f.: (1-3x+x^2-sqrt(1-10x+19x^2-10x^3+x^4))/(2x);

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

a(n) = sum{k=0..n, (0^(n+k)+C(n+k-1,2k-1))*A006318(k)}=0^n + sum{k=0..n, C(n+k-1,2k-1)*A006318(k)}.

Conjecture: (n+1)*a(n) +5*(1-2n)*a(n-1) +19*(n-2)*a(n-2) +5*(7-2*n)*a(n-3) +(n-5)*a(n-4)=0. - R. J. Mathar, Nov 16 2011

Mathematica

CoefficientList[Series[(1 - 3*t + t^2 - Sqrt[1 - 10*t + 19*t^2 - 10*t^3 + t^4])/(2*t), {t, 0, 50}], t] (* G. C. Greubel, May 23 2016 *)

Crossrefs

Sequence in context: A360317 A074612 A104497 * A238796 A216340 A080117

Adjacent sequences: A166691 A166692 A166693 * A166695 A166696 A166697

Keyword

easy,nonn

Author

Paul Barry, Oct 18 2009

Status

approved