A342988 Number of tree-rooted planar maps with n edges and no isthmuses.

1, 1, 4, 23, 162, 1292, 11214, 103497, 1000810, 10039100, 103725188, 1098151276, 11866435816, 130477138014, 1456320910090, 16468167354971, 188369396046810, 2176619115192140, 25379588118629856, 298341351434460488, 3532848638781046852, 42113699799069958732

Offset: 0

Author

Andrew Howroyd, Apr 03 2021

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..500

Crossrefs

Row sums of A342987.

Cf. A004304, A342986.

Programs

PARI

\\ here J(n) gives A004304 as g.f.
J(n)={my(g=(1-sqrt(1-4*x+O(x^3*x^n)))/(2*x), h=serconvol(g, (g-1)/x)); sqrt(x/serreverse(x*h^2))}
seq(n)={my(g=J(n)-x, p=O(1)); while(serprec(p, x)<=n, p = subst(g, x, x*p^2)); Vec(p)}

Formula

G.f.: A(x) satisfies A(x) = G(x*A(x)^2) where G(x) + x is the g.f. of A004304.