A287891
Number of rooted unlabeled 4-cactus graphs on 3n+1 nodes.
Original entry on oeis.org
1, 1, 3, 11, 46, 208, 1002, 5012, 25863, 136519, 733902, 4003475, 22106155, 123313289, 693871975, 3933700703, 22447035938, 128828019447, 743142630614, 4306327193744, 25056121416684, 146325789652514, 857393585946194, 5039223717251954, 29700183601347111, 175496470696059267
Offset: 0
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EulerT(v)={Vec(exp(x*Ser(dirmul(v,vector(#v,n,1/n))))-1, -#v)}
seq(n)={my(v=[]); for(n=1, n, my(g=1+x*Ser(v)); v=EulerT(Vec(g*(g^2 + subst(g, x, x^2))/2))); concat([1], v)} \\ Andrew Howroyd, Feb 17 2020
a(0) changed and terms a(11) and beyond from
Andrew Howroyd, Feb 17 2020
A287892
Number of unrooted unlabeled 4-cactus graphs on 3n+1 nodes.
Original entry on oeis.org
1, 1, 1, 3, 7, 25, 88, 366, 1583, 7336, 34982, 172384, 867638, 4452029, 23194392, 122462546, 653957197, 3527218134, 19192275883, 105248481503, 581223149532, 3230039198628, 18053111982952, 101426901301489, 572554846192811, 3246191706162233, 18478844801342495
Offset: 0
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\\ Here G(n) is A287891 as vector.
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
G(n)={my(v=[]); for(n=1, n, my(g=1+x*Ser(v)); v=EulerT(Vec(g*(g^2 + subst(g, x, x^2))/2))); concat([1], v)}
seq(n)={my(p=Ser(G(n))); my(g(d)=subst(p,x,x^d)); Vec(g(1) + x*(2*g(4) + 3*g(2)^2 - 2*g(1)^2*g(2) - 3*g(1)^4)/8)} \\ Andrew Howroyd, Feb 18 2020
a(0) changed and terms a(12) and beyond from
Andrew Howroyd, Feb 18 2020
A287890
Number of unrooted labeled 4-cactus graphs on 3n+1 nodes.
Original entry on oeis.org
1, 3, 630, 756000, 2740537800, 22317642547200, 344030189461358400, 8979238155223784448000, 366881017725878906250000000, 22141857318039212329716940800000, 1887349497873286715447530129178400000, 219275034010568207287452830493455155200000
Offset: 0
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[(3*n+1)^(n-1)*Factorial(3*n)/(2^n*Factorial(n)): n in [0..12]]; // Vincenzo Librandi, Feb 19 2020
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Table[(3 n + 1)^(n-1) (3 n)! / (2^n n!), {n, 0, 15}] (* Vincenzo Librandi, Feb 19 2020 *)
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seq(n)={my(p=serlaplace(serreverse(x*exp(-x^3/2 + O(x^(3*n+1))))/x)); vector(n+1, k, polcoef(p, 3*k-3))} \\ Andrew Howroyd, Feb 17 2020
a(0) changed and terms a(7) and beyond from
Andrew Howroyd, Feb 17 2020
Showing 1-3 of 3 results.