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A137265
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G.f. y(x) is solution of x y^3 - (1 + x^2) y + 1 = 0 with y(0) = 1.
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0
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1, 1, 2, 8, 35, 163, 796, 4024, 20885, 110654, 596064, 3254752, 17974893, 100227022, 563482140, 3190633232, 18179765509, 104158703503, 599698459613, 3467978715612, 20134256546896, 117313279477959, 685756774642494
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(0) = 1, a(1) = 1, a(n) = -a(n-2) + sum_{i=0}^{n-1} sum_{j=0}^{n-1-i} a(i) a(j) a(n-1-i-j)
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EXAMPLE
| a(3) = 8 because g(x) = 1 + x + 2 x^2 + 8 x^3 + O(x^4) satisfies
x g(x)^3 - (1 + x^2) g(x) + 1 = O(x^4)
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MAPLE
| f:= (x, y) -> x*y^3 - (1 + x^2)*y + 1; N:= (y, n) -> convert(normal(taylor(y-f(x, y)/D[2](f)(x, y), x=0, n)), polynom); Y:= 1; for j from 1 to 6 do Y:= N(Y, 2^j) end do; seq(coeftayl(Y, x=0, j), j=0..2^6-1);
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MATHEMATICA
| max = 22; g[x_] := Sum[a[k]*x^k, {k, 0, max}]; coes = CoefficientList[ Series[ x*g[x]^3 - (1+x^2)*g[x] + 1, {x, 0, max}], x]; sol = First[ Solve[ Thread[ coes == 0 ] ] ]; Table[a[n] /. sol, {n, 0, max}](* From Jean-François Alcover, Nov 28 2011 *)
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CROSSREFS
| Sequence in context: A037618 A184786 A082759 * A129580 A007034 A011791
Adjacent sequences: A137262 A137263 A137264 * A137266 A137267 A137268
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KEYWORD
| easy,nonn
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AUTHOR
| Robert B. Israel (israel(AT)math.ubc.ca), Mar 12 2008
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