A379435 Number of rooted planar maps with n edges and without faces or vertices of degree 1.
1, 0, 1, 2, 10, 52, 281, 1570, 9022, 53084, 318634, 1945396, 12052532, 75624616, 479814937, 3074251682, 19869323638, 129420288076, 848897059790, 5603350613308, 37198680816844, 248241480270680, 1664546969372554, 11210468046615412, 75806810042727980, 514537522249147672
Offset: 0
Keywords
Programs
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PARI
seq(n)={my(z=x/(1 + 2*x)^2, g=(-1 + 18*z + sqrt(1-12*z + O(x^(n+3)))^3) / (54*z^2)); Vec(2*x + g*(1-2*x)/(1+2*x))}
Formula
G.f.: 2*x + G(x/(1 + 2*x)^2)*(1 - 2*x)/(1 + 2*x) where G(x) is the g.f. of A000168.