A115153 Sixth diagonal (M=6) sequence of triangle A113647, called Y(2,1).

1, 127, 1665, 16255, 141441, 1163135, 9273473, 72613759, 562430081, 4327407487, 33161347201, 253517365119, 1935665528961, 14771256557439, 112715410440321, 860346088685439, 6570305359184001, 50209563856600959, 383989436028813441

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n)= A113647(n+5, n+1), n>=0.

G.f.: ((-2 + 16*x - 24*x^2 + x^5) + 2*(1 - 10*x + 24*x^2 - 8*x^3)*c(2*x))/((x^5)*(1+x)), with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers).

Recurrence: (n-1)*(n+6)*a(n) = (7*n^2+23*n+30)*a(n-1) + 4*(n+2)*(2*n+3)*a(n-2). - Vaclav Kotesovec, Oct 19 2012

a(n) ~ 7*2^(3n+13)/(9*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 19 2012

Mathematica

CoefficientList[Series[((-2+16*x-24*x^2+x^5)+2*(1-10*x+24*x^2-8*x^3)*(1-Sqrt[1-8*x])/(4*x))/((x^5)*(1+x)), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 19 2012 *)

Crossrefs

Sequence in context: A258012 A258002 A025598 * A172408 A204216 A075937

Adjacent sequences: A115150 A115151 A115152 * A115154 A115155 A115156

Keyword

nonn,easy

Author

Wolfdieter Lang, Jan 13 2006

Status

approved