A247660 Number of bi-indecomposable topologies on n labeled points.
1, 2, 15, 229, 5298, 177661, 8605831, 601894158, 60571434501, 8716575772821, 1780241773757704, 511992638746006383, 205785031866223973343, 114780183140747719353332, 88271680420025831479693219, 93054995762621287409298093049
Offset: 1
Keywords
Links
- L. Foissy and C. Malvenuto, The Hopf algebra of finite topologies and T-partitions, arXiv preprint arXiv:1407.0476 [math.RA], 2014.
Programs
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Mathematica
A000798 = {1, 1, 4, 29, 355, 6942, 209527, 9535241, 642779354, 63260289423, 8977053873043, 1816846038736192, 519355571065774021, 207881393656668953041, 115617051977054267807460, 88736269118586244492485121, 93411113411710039565210494095, 134137950093337880672321868725846, 261492535743634374805066126901117203}; f[x_] = Sum[A000798[[n+1]] x^n, {n, 0, nmax = Length[A000798]-1}]; CoefficientList[(-2 + 3 f[x] - f[x]^2)/f[x] + O[x]^nmax, x][[2 ;; -2]] (* Jean-François Alcover, Oct 10 2018 *)
Formula
G.f.: (-2+3*f(x)-f(x)^2)/f(x), where f(x) is the g.f. of A000798.