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A275787 Number of cells in the two-sided Coxeter complex of type B_n. 2
1, 5, 41, 509, 8469, 176217, 4400325, 128203049, 4268957449, 159922273421, 6656731517249, 304797275277365, 15224868078068845, 823874409422614577, 48012621942105876301, 2997884066292303095889, 199666128081901473290833, 14129411123649333432720277, 1058688691179737704258634521, 83732563305101190468369022317, 6971039973751002759723517967941 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..21.

Evgeniy Krasko, Counting Unlabelled Chord Diagrams of Maximal Genus, arXiv:1709.00796 [math.CO], 2017.

T. K. Petersen, A two-sided analogue of the Coxeter complex, arXiv:1607.00086 [math.CO], (2016)

MAPLE

B:=proc(n) local f;

option remember;

if n=1 then 1+s*t;

elif n>1 then

f:=B(n-1);

RETURN(simplify( (2*n*s*t-s*t+1)*f+(2*s*t*(1-s)+s/n*(1-s)*(1-t))*diff(f, s) + (2*s*t*(1-t)+t/n*(1-s)*(1-t))*diff(f, t) + 2/n*s*t*(1-s)*(1-t)*diff( diff(f, s), t) ));

fi;

end:

seq(eval(eval(subs(s=x/(1+x), t=y/(1+y), B(n))*(1+x)^n*(1+y)^n, y=1), x=1), n=1..30);

MATHEMATICA

B[n_] := B[n] = Which[n == 1, 1 + s*t, n > 1, f = B[n - 1]; Return[ Simplify[ (2*n*s*t - s*t + 1)*f + (2*s*t*(1 - s) + s/n*(1 - s)*(1 - t))*D[f, s] + (2*s*t*(1 - t) + t/n*(1 - s)*(1 - t))*D[f, t] + 2/n*s*t*(1 - s)*(1 - t)*D[ D[f, s], t]]]];

Join[{1}, Table[bn = ((B[n] /. {s -> x/(1 + x), t -> y/(1 + y)})*(1 + x)^n*(1 + y)^n /. {y -> 1, x -> 1}); Print[bn]; bn, {n, 1, 20}]] (* Jean-Fran├žois Alcover, Nov 27 2017, from Maple *)

CROSSREFS

Cf. A120733 gives the number of cells for type A_n.

Sequence in context: A240996 A143415 A056545 * A009755 A000685 A144286

Adjacent sequences:  A275784 A275785 A275786 * A275788 A275789 A275790

KEYWORD

nonn

AUTHOR

Kyle Petersen, Aug 09 2016

STATUS

approved

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Last modified February 15 16:25 EST 2019. Contains 320136 sequences. (Running on oeis4.)