A035351 Number of labeled rooted polygonal cacti with bridges (mixed Husimi trees) with n nodes.

1, 2, 12, 124, 1810, 34056, 783874, 21331136, 669902076, 23845794400, 948733833256, 41721533664768, 2009539243299328, 105209055401980544, 5948937678563109000, 361296961279074942976, 23456120142707873968336, 1621073894248128387746304

Offset

1,2

Links

Alois P. Heinz, Table of n, a(n) for n = 1..100

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) = x*exp((2*A(x)-A(x)^2)/(2-2*A(x))).

a(n) ~ (1-s)^2 * sqrt(2/((2-s)*(1+s-s^2))) * n^(n-1) / (s * exp((2+(s-4)*s)/(2-2*s)))^n, where s = 1/3*(4-2/(-17+3*sqrt(33))^(1/3) + (-17+3*sqrt(33))^(1/3)) = 0.456310987307923638429144... is the root of the equation 6*s - 4*s^2 + s^3 = 2. - Vaclav Kotesovec, Jan 08 2014

Maple

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

Mathematica

Rest[CoefficientList[InverseSeries[Series[x/E^(((x-2)*x)/(2*(x-1))), {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 08 2014 *)

Crossrefs

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

Sequence in context: A214223 A173219 A227458 * A209627 A253282 A375899

Adjacent sequences: A035348 A035349 A035350 * A035352 A035353 A035354

Keyword

nonn,eigen

Author

Christian G. Bower, Nov 15 1998

Extensions

More terms from Alois P. Heinz, Aug 20 2008

Status

approved