A115150 Third diagonal (M=3) sequence of triangle A113647, called Y(2,1).

1, 15, 113, 783, 5361, 36879, 255985, 1794063, 12689393, 90505231, 650379249, 4705157135, 34244198385, 250572963855, 1842382110705, 13605619630095, 100872203796465, 750556607938575, 5602962592235505, 41952165966643215

Offset: 0

Author

Wolfdieter Lang, Jan 13 2006

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300

Crossrefs

a(n)=A115138(n+2), n>=0.

Programs

Mathematica

CoefficientList[Series[((4*x-2+x^2)+2*(1-4*x)*(1-Sqrt[1-8*x])/(4*x))/((x^2)*(1+x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

Formula

a(n)= A113647(n+2, n+1), n>=0.

G.f.: ((4*x-2+x^2) + 2*(1-4*x)*c(2*x))/((x^2)*(1+x)), with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).

Recurrence: (n-1)*(n+3)*a(n) = (7*n^2 + 2*n + 3)*a(n-1) + 4*n*(2*n+1)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 2^(3*n+9)/(9*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012