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

0,3

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) + 2*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)-2*x, p=O(1)); while(serprec(p, x)<=n, p = subst(g, x, x*p^2)); Vec(p)}

Crossrefs

Row sums of A342985.

Cf. A004304, A342988.

Sequence in context: A077259 A319112 A371493 * A136589 A077048 A354309

Adjacent sequences: A342983 A342984 A342985 * A342987 A342988 A342989

Keyword

nonn

Author

Andrew Howroyd, Apr 03 2021

Status

approved