A342986 Number of tree-rooted loopless planar maps with n edges and no isthmuses.

1, 0, 2, 6, 44, 280, 2100, 16310, 133652, 1132992, 9895672, 88520520, 808057712, 7504219008, 70730676392, 675328163542, 6521495669380, 63612394972608, 626076210568200, 6211621325369992, 62077602307372720, 624488579671582880, 6320044589443116720, 64313288809475362888

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 A342985.

Cf. A004304, A342988.

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)-2*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) + 2*x is the g.f. of A004304.