

A091488


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


3



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
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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)^(n1)/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 A007561 A274295
Adjacent sequences: A091485 A091486 A091487 * A091489 A091490 A091491


KEYWORD

nonn,eigen


AUTHOR

Christian G. Bower, Jan 14 2004


STATUS

approved



