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

Author

N. J. A. Sloane, Jan 04 2014

Keywords

• nonn

Links

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

Crossrefs

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

Programs

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 *)

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

Extensions

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