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A361244
Number of noncrossing bridgeless cacti with n nodes.
2
1, 1, 0, 1, 1, 6, 13, 57, 169, 673, 2301, 8933, 32747, 127063, 483484, 1889957, 7352241, 29003446, 114481435, 455542880, 1816976042, 7285391071, 29291855748, 118218771203, 478372112363, 1941436590561, 7897802784418, 32205683248225, 131602039333873
OFFSET
0,6
FORMULA
G.f. 1 + A(x) where A(x) satisfies A(x) = x^2*(x - A(x)^2)/(x^2 - x*A(x)^2 - A(x)^4).
PROG
(PARI) seq(n)={my(g=1+O(x)); for(n=1, n\2, g=1/(1 - x^2*g^4/(1 - x*g^2))); Vec(1 + x*g + O(x*x^n))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Andrew Howroyd, Mar 08 2023
STATUS
approved