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

0,2

Links

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

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

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 *)

Crossrefs

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

Sequence in context: A110822 A222410 A001849 * A115138 A233326 A092317

Adjacent sequences: A115147 A115148 A115149 * A115151 A115152 A115153

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 13 2006

Status

approved