A238299 Second convolution of A107841.
1, 4, 24, 164, 1208, 9348, 74920, 616420, 5176296, 44182916, 382205048, 3343343268, 29523386968, 262826367748, 2356256046216, 21254326842596, 192766180154120, 1756758963727620, 16079466335134168, 147748236828875428, 1362397741935948024, 12603116216808465284, 116929440001191010664
Offset: 0
Links
- Fung Lam, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
CoefficientList[Series[((1 + x - Sqrt[1 - 10*x + x^2])/(6*x))^2, {x, 0, 100}], x] (* Vaclav Kotesovec, Feb 27 2014 *)
Formula
G.f.: (G.f. of A107841)^2.
Recurrence: (n+2)*a(n) = (4-n)*a(n-4) + 4*(2*n-5)*a(n-3) + 18*(n-1)*a(n-2) + 4*(2*n+1)*a(n-1), n>=4.
Recurrence (of order 2): (n+2)*(2*n-1)*a(n) = 4*(5*n^2-2)*a(n-1) - (n-2)*(2*n+1)*a(n-2). - Vaclav Kotesovec, Feb 27 2014
a(n) ~ sqrt(360+147*sqrt(6)) * (5+2*sqrt(6))^n / (9 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 27 2014