A115137 Second diagonal of triangle A113647 (called Y(2,1)).

1, 1, 7, 41, 247, 1545, 9975, 66057, 446455, 3067913, 21372919, 150618121, 1071841271, 7691763721, 55600938999, 404488323081, 2959189475319, 21757613309961, 160691417776119, 1191577871450121, 8868160862158839

Offset: 0

Author

Wolfdieter Lang, Jan 13 2006

Keywords

• nonn
• easy

Examples

			41=a(3)= A062992(3) - 2*A062992(2) = 67 - 2*13.
		

Links

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

Programs

Mathematica

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

Formula

a(n)= b(n) - 2*b(n-1) with b(n):=A062992(n)= A064062(n+1), n>=1. a(0):=1.

G.f.: (1-2*x)*(2*c(2*x)-1)/(1+x) with c(x) g.f. of A000108 (Catalan).

a(n)= A113647(n, n), n>=1.

Recurrence: (n-2)*(n+1)*a(n) = (7*n^2-19*n+14)*a(n-1) + 4*(n-1)*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

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