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

0,3

Links

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

Formula

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

Prog

(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)}

Crossrefs

Row sums of A342987.

Cf. A004304, A342986.

Sequence in context: A182969 A263186 A245110 * A304074 A307402 A354497

Adjacent sequences: A342985 A342986 A342987 * A342989 A342990 A342991

Keyword

nonn

Author

Andrew Howroyd, Apr 03 2021

Status

approved