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 A115152 Fifth diagonal (M=5) sequence of triangle A113647, called Y(2,1). 0

%I

%S 1,63,705,6207,50113,389183,2965441,22380607,168132545,1260716095,

%T 9450356673,70882689087,532259536833,4002476458047,30145737916353,

%U 227429364793407,1718693633458113,13009919057854527,98641252341252033

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

%H Vincenzo Librandi, <a href="/A115152/b115152.txt">Table of n, a(n) for n = 0..300</a>

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

%F 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).

%F 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

%F a(n) ~ 2^(3*n+12)/(3*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 19 2012

%t 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 *)

%K nonn,easy,changed

%O 0,2

%A _Wolfdieter Lang_, Jan 13 2006

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