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

Author

Andrew Howroyd, Jan 14 2025

Keywords

• nonn

Crossrefs

Cf. A000168, A006388 (sensed), A006389 (unsensed), A379434, A379435.

Programs

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.