A091488 Number of asymmetric rooted 2,3 cacti (triangular cacti with bridges).

1, 1, 1, 3, 6, 16, 42, 115, 319, 909, 2614, 7622, 22422, 66556, 198946, 598617, 1811205, 5508015, 16825307, 51605568, 158860950, 490666293, 1520106655, 4722502437, 14708971581, 45921804883, 143682973435, 450477673623

Offset

1,4

Comments

Also asymmetric involution rooted trees.

Links

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

N. J. A. Sloane, Transforms

Index entries for sequences related to cacti

Index entries for sequences related to rooted trees

Formula

Shifts left under transform T where Ta = WEIGH(W_1, 2(a)). W_1, 2(a) has g.f. A(x)+(A(x^2)-A(x)^2)/2.

Prog

(PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, (-1)^(n-1)/n))))-1, -#v)}
seq(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))))); Vec(p)} \\ Andrew Howroyd, Aug 30 2018

Crossrefs

Cf. A091486, A091489.

Sequence in context: A027102 A218207 A019497 * A202839 A371705 A007561

Adjacent sequences: A091485 A091486 A091487 * A091489 A091490 A091491

Keyword

nonn,eigen

Author

Christian G. Bower, Jan 14 2004

Status

approved