A247659 Number of down-arrow-indecomposable topologies on n labeled points.

1, 3, 22, 292, 6120, 193594, 9070536, 622336756, 61915861962, 8846814822932, 1798543906246948, 515674104905890202, 206833212761446463192, 115198617558900993580396, 88503974769306037986089170, 93233054587165663487254293572

Offset: 1

Author

N. J. A. Sloane, Oct 05 2014

Keywords

• nonn

Links

• L. Foissy and C. Malvenuto, The Hopf algebra of finite topologies and T-partitions, arXiv preprint arXiv:1407.0476, 2014

Crossrefs

Cf. A000598, A247660.

Programs

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[(f[x]-1)/f[x] + O[x]^nmax, x][[2 ;; -2]] (* Jean-François Alcover, Oct 10 2018 *)

Formula

G.f.: (A000798(x)-1)/A000798(x), where A000798(x) is the g.f. of A000798.