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%I #10 May 22 2013 05:47:18
%S 1,1,7,41,247,1545,9975,66057,446455,3067913,21372919,150618121,
%T 1071841271,7691763721,55600938999,404488323081,2959189475319,
%U 21757613309961,160691417776119,1191577871450121,8868160862158839
%N Second diagonal of triangle A113647 (called Y(2,1)).
%H Vincenzo Librandi, <a href="/A115137/b115137.txt">Table of n, a(n) for n = 0..300</a>
%F a(n)= b(n) - 2*b(n-1) with b(n):=A062992(n)= A064062(n+1), n>=1. a(0):=1.
%F G.f.: (1-2*x)*(2*c(2*x)-1)/(1+x) with c(x) g.f. of A000108 (Catalan).
%F a(n)= A113647(n, n), n>=1.
%F Recurrence: (n-2)*(n+1)*a(n) = (7*n^2-19*n+14)*a(n-1) + 4*(n-1)*(2*n-3)*a(n-2). - _Vaclav Kotesovec_, Oct 19 2012
%F a(n) ~ 2^(3*n+2)/(3*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 19 2012
%e 41=a(3)= A062992(3) - 2*A062992(2) = 67 - 2*13.
%t CoefficientList[Series[(1-2*x)*(2*(1-Sqrt[1-8*x])/(4*x)-1)/(1+x), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Oct 19 2012 *)
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, Jan 13 2006