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%I #10 May 22 2013 05:47:05
%S 1,127,1665,16255,141441,1163135,9273473,72613759,562430081,
%T 4327407487,33161347201,253517365119,1935665528961,14771256557439,
%U 112715410440321,860346088685439,6570305359184001,50209563856600959,383989436028813441
%N Sixth diagonal (M=6) sequence of triangle A113647, called Y(2,1).
%H Vincenzo Librandi, <a href="/A115153/b115153.txt">Table of n, a(n) for n = 0..200</a>
%F a(n)= A113647(n+5, n+1), n>=0.
%F 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).
%F 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
%F a(n) ~ 7*2^(3n+13)/(9*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 19 2012
%t 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 *)
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Jan 13 2006
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