A035352 Number of increasing rooted polygonal cacti with bridges (mixed Husimi trees) with n nodes.

1, 1, 3, 16, 122, 1203, 14518, 207061, 3406083, 63465271, 1320938774, 30371545338, 764447981599, 20904838435264, 617151430504113, 19561785238965715, 662583041367287249, 23882958184429006800, 912777131398463190802, 36868849734952579404745

Offset

1,3

Comments

Limit n->infinity (a(n)/n!)^(1/n) = 2.168573... - Vaclav Kotesovec, Feb 28 2014

Links

Alois P. Heinz, Table of n, a(n) for n = 1..200

Index entries for sequences related to cacti

Index entries for sequences related to rooted trees

Index entries for sequences related to trees

Formula

E.g.f. satisfies A'(x) = exp((2*A(x)-A(x)^2)/(2-2*A(x))).

Maple

Ap:= proc(n) option remember; local A, f; if n<=0 then f:=1 else A:= Int(Ap(n-1), x); f:= exp((2*A -A^2)/ (2-2*A)) fi; convert(series(f, x, n+1), polynom) end: a:= n-> coeff(series(Ap(n-1), x=0, n), x, n-1)*(n-1)!: seq(a(n), n=1..30); # Alois P. Heinz, Aug 20 2008

Mathematica

Ap[n_] := Ap[n] = Module[{A, f}, If[n <= 0, f=1, A = Integrate[Ap[n-1], x]; f = Exp[(2*A-A^2)/(2-2*A)]]; Series[f, {x, 0, n+1}] // Normal]; a[n_] := SeriesCoefficient[Ap[n-1], {x, 0, n-1}]*(n-1)!; Table[a[n], {n, 1, 30}] (* Jean-François Alcover, Feb 24 2016, after Alois P. Heinz *)

Crossrefs

Cf. A000083, A000237, A000314, A035082, A035349-A035357.

Sequence in context: A141625 A053588 A295928 * A159607 A087018 A005119

Adjacent sequences: A035349 A035350 A035351 * A035353 A035354 A035355

Keyword

nonn,eigen

Author

Christian G. Bower, Nov 15 1998

Extensions

a(18) corrected by Alois P. Heinz, Aug 20 2008

Status

approved