A115152 Fifth diagonal (M=5) sequence of triangle A113647, called Y(2,1).

1, 63, 705, 6207, 50113, 389183, 2965441, 22380607, 168132545, 1260716095, 9450356673, 70882689087, 532259536833, 4002476458047, 30145737916353, 227429364793407, 1718693633458113, 13009919057854527, 98641252341252033

Offset

0,2

Links

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

Formula

a(n)= A113647(n+4, n+1), n>=0.

G.f.: ((-2 + 12*x - 8*x^2 + x^4) + 2*(1-8*x+12*x^2)*c(2*x))/((x^4)*(1+x)), with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).

Recurrence: (n-1)*(n+5)*a(n) = (7*n^2+16*n+17)*a(n-1) + 4*(n+1)*(2*n+3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 2^(3*n+12)/(3*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012

Mathematica

CoefficientList[Series[((-2+12*x-8*x^2+x^4)+2*(1-8*x+12*x^2)*(1-Sqrt[1-8*x])/(4*x))/((x^4)*(1+x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

Crossrefs

Sequence in context: A086578 A198399 A221968 * A343978 A371878 A284953

Adjacent sequences: A115149 A115150 A115151 * A115153 A115154 A115155

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 13 2006

Status

approved