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A091489 Number of asymmetric 2,3 cacti (triangular cacti with bridges). 3
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 (list; graph; refs; listen; history; text; internal format)
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 * A047087 A104779 A178718

Adjacent sequences:  A091486 A091487 A091488 * A091490 A091491 A091492

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 14 2004

STATUS

approved

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Last modified June 5 06:41 EDT 2020. Contains 334828 sequences. (Running on oeis4.)