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

1,7

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Index entries for sequences related to cacti

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

Prog

(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

Crossrefs

Cf. A091487, A091488.

Sequence in context: A307251 A320803 A262184 * A104779 A178718 A244897

Adjacent sequences: A091486 A091487 A091488 * A091490 A091491 A091492

Keyword

nonn

Author

Christian G. Bower, Jan 14 2004

Status

approved