A091489 Number of asymmetric 2,3 cacti (triangular cacti with bridges).

1, 0, 0, 0, 0, 1, 3, 7, 21, 57, 159, 435, 1217, 3400, 9633, 27413, 78733, 227489, 661984, 1937211, 5701733, 16865522, 50126650, 149627241, 448448400, 1349060262, 4072508115, 12333762442, 37466367898, 114133581762

Offset: 1

Author

Christian G. Bower, Jan 14 2004

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..500
• Index entries for sequences related to cacti

Crossrefs

Cf. A091487, A091488.

Programs

PARI

WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}
b(n)={my(p=O(x)); for(n=1, n, p=x+x^2*(Ser(WeighT(Vec(p + (p^2 - subst(p,x,x^2))/2))))); p}
seq(n)={my(p=b(n)); Vec(p - p^2/2 - p^3/3 - subst(p, x, x^2)/2 + subst(p, x, x^3)/3)} \\ Andrew Howroyd, Aug 30 2018

Formula

G.f.: A(x) = B(x)-B(x)^2/2-B(x^2)/2+B(x^3)/3-B(x)^3/3 where B is g.f. of A091488