A370800 Expansion of (1/x) * Series_Reversion( x/(x+1/(1-x+x^3)) ).
1, 2, 5, 14, 41, 120, 337, 855, 1671, 434, -20393, -158032, -885329, -4322580, -19407365, -81796098, -325964629, -1226861808, -4319079961, -13880383674, -38282558205, -72411121618, 65816173987, 1746824677851, 12859713835981, 73356840199948, 369390356474509
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serreverse(x/(x+1/(1-x+x^3)))/x)
Formula
a(n) = Sum_{k=0..n} binomial(n,k) * b(k), where g.f. B(x) = Sum_{k>=0} b(k)*x^k satisfies B(x) = (1/x) * Series_Reversion( x*(1-x+x^3) ).