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A273034
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G.f. A(x) satisfies: A(x*A(-x)) = x^3 - x^2.
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1
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1, 1, 1, 2, 2, 3, 5, 9, 18, 38, 79, 162, 330, 661, 1323, 2661, 5392, 11037, 22802, 47447, 99238, 208283, 438143, 923325, 1949051, 4121495, 8731982, 18536690, 39428284, 84023511, 179370023, 383518886, 821198510, 1760683462, 3779593676, 8122853103, 17476215940, 37639236974, 81146453958, 175111467257, 378230792221, 817669121153, 1769125092131, 3830738971497, 8301063679980, 18001035450869, 39062530229674, 84822294102377, 184304055379313, 400704466515940
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OFFSET
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1,4
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LINKS
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EXAMPLE
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G.f.: A(x) = x + x^2 + x^3 + 2*x^4 + 2*x^5 + 3*x^6 + 5*x^7 + 9*x^8 + 18*x^9 + 38*x^10 + 79*x^11 + 162*x^12 + 330*x^13 + 661*x^14 + 1323*x^15 + 2661*x^16 +...
such that A(x*A(-x)) = x^3 - x^2.
RELATED SERIES.
Let B(x) be the series reversion of g.f. A(x), so that A(B(x)) = x, then
B(x) = x - x^2 + x^3 - 2*x^4 + 6*x^5 - 17*x^6 + 45*x^7 - 123*x^8 + 356*x^9 - 1061*x^10 + 3193*x^11 - 9691*x^12 + 29741*x^13 - 92228*x^14 +...+ (-1)^(n-1)*A268655(n)*x^n +...
where B(x^3 - x^2) = x*A(-x),
also, B(B(x^3-x^2)/x) = -x.
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PROG
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(PARI) {a(n) = my(A=[1, 1], F); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A] = Vec(subst(F, x, -x*F))[#A]); A[n]}
for(n=1, 50, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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