A379433 Number of rooted planar maps with n edges and without faces of degree 1.
1, 1, 3, 16, 96, 624, 4304, 31056, 232128, 1784752, 14043312, 112648848, 918456608, 7593649392, 63546379152, 537427956688, 4587713701248, 39488179213872, 342414691125104, 2989022121125136, 26249475365186016, 231786459869636464, 2056950693208881744
Offset: 0
Keywords
Programs
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PARI
seq(n)={my(z=x/(1 + x)^2, g=(-1 + 18*z + sqrt(1-12*z + O(x^(n+3)))^3) / (54*z^2)); Vec(x + g*(1-x)/(1+x))}
Formula
G.f.: x + G(x/(1 + x)^2)*(1 - x)/(1 + x) where G(x) is the g.f. of A000168.