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

0,3

Links

Table of n, a(n) for n=0..22.

Formula

G.f.: x + G(x/(1 + x)^2)*(1 - x)/(1 + x) where G(x) is the g.f. of A000168.

Prog

(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))}

Crossrefs

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

Sequence in context: A006347 A000270 A157051 * A000271 A157016 A228792

Adjacent sequences: A379430 A379431 A379432 * A379434 A379435 A379436

Keyword

nonn

Author

Andrew Howroyd, Jan 14 2025

Status

approved