A234938 Coefficients of Hilbert series for the suboperad of bicolored noncrossing configurations generated by a fully colored triangle and a fully uncolored triangle.

1, 2, 8, 40, 216, 1246, 7516, 46838, 299200, 1948804, 12893780, 86415940, 585461380, 4003022222, 27587072156, 191426864328, 1336331235624, 9378578814890, 66133103587412, 468323884345060, 3329180643569660, 23748479467116032, 169944228206075568, 1219639212041064130

Offset

1,2

Links

Table of n, a(n) for n=1..24.

Frédéric Chapoton and Samuele Giraudo, Enveloping operads and bicoloured noncrossing configurations, arXiv preprint arXiv:1310.4521 [math.CO], 2013-2014.

Formula

G.f. A(t) satisfies 4t-2t^2-t^3+t^4 + (-4+4t-t^2+2t^3)*A(t) + (6+t)*A(t)^2 + (1-2t)*A(t)^3 - A(t)^4 = 0 [Chapoton & Giraudo, Proposition 3.5]. - Andrey Zabolotskiy, Feb 02 2025

Mathematica

Rest@CoefficientList[Root[Function[{f}, 4t-2t^2-t^3+t^4 + (-4+4t-t^2+2t^3)f + (6+t)f^2 + (1-2t)f^3 - f^4], 2] + O[t]^25, t] (* Andrey Zabolotskiy, Feb 02 2025 *)

Crossrefs

Cf. A234939, A052701, A007863, A006013, A006318.

Sequence in context: A025570 A227081 A113449 * A143388 A027282 A006195

Adjacent sequences: A234935 A234936 A234937 * A234939 A234940 A234941

Keyword

nonn

Author

N. J. A. Sloane, Jan 04 2014

Extensions

Terms a(9) onwards added and name clarified by Andrey Zabolotskiy, Feb 02 2025

Status

approved