cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A091489 Number of asymmetric 2,3 cacti (triangular cacti with bridges).

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%I A091489 #10 Aug 30 2018 18:56:22
%S A091489 1,0,0,0,0,1,3,7,21,57,159,435,1217,3400,9633,27413,78733,227489,
%T A091489 661984,1937211,5701733,16865522,50126650,149627241,448448400,
%U A091489 1349060262,4072508115,12333762442,37466367898,114133581762
%N A091489 Number of asymmetric 2,3 cacti (triangular cacti with bridges).
%H A091489 Andrew Howroyd, <a href="/A091489/b091489.txt">Table of n, a(n) for n = 1..500</a>
%H A091489 <a href="/index/Ca#cacti">Index entries for sequences related to cacti</a>
%F A091489 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
%o A091489 (PARI) WeighT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v,n,(-1)^(n-1)/n))))-1,-#v)}
%o A091489 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}
%o A091489 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
%Y A091489 Cf. A091487, A091488.
%K A091489 nonn
%O A091489 1,7
%A A091489 _Christian G. Bower_, Jan 14 2004