A113956 Expansion of (1/((1-4x)c(x)))/(1-x^2c(x)/sqrt(1-4x)), c(x) the g.f. of A000108.
1, 3, 12, 48, 194, 787, 3199, 13017, 52997, 215831, 879076, 3580511, 14582842, 59388280, 241829963, 984609111, 4008282780, 16315179752, 66399357417, 270193396769, 1099323033137, 4472155924094, 18190769442979, 73982564102230
Offset: 0
Programs
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Mathematica
CoefficientList[Series[(1+Sqrt[1-4x])/(2-x(7+Sqrt[1-4x]+4x)),{x,0,30}],x] (* Harvey P. Dale, Feb 10 2015 *)
Formula
G.f.: (1+sqrt(1-4x))/(sqrt(1-4x)(sqrt(1-4x)(x+2)-x)); a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(j, j-k)C(2n-2k, n-k-j)}}.
Conjecture D-finite with recurrence: n*a(n) +2*(-5*n+4)*a(n-1) +(27*n-46)*a(n-2) +(5*n-2)*a(n-3) +(-57*n+188)*a(n-4) +2*(-21*n+83)*a(n-5) +4*(-2*n+9)*a(n-6)=0. - R. J. Mathar, Jan 24 2020
Comments