%I #10 Jan 21 2020 04:37:20

%S 1,2,9,44,195,804,3185,12368,47607,182720,701349,2695978,10384231,

%T 40083848,155052001,600949336,2333344095,9074611032,35344215245,

%U 137844431690,538253680159,2104090575136,8233413950409

%N Number of commutative elements in Coxeter group H_n.

%D C. Kenneth Fan, Structure of a Hecke algebra quotient. J. Amer. Math. Soc. 10 (1997), no. 1, 139-167.

%D C. K. Fan, A Hecke algebra quotient and some combinatorial applications. J. Algebraic Combin. 5 (1996), no. 3, 175-189.

%H Boothby, T.; Burkert, J.; Eichwald, M.; Ernst, D. C.; Green, R. M.; Macauley, M. <a href="https://doi.org/10.1007/s10801-011-0327-z">On the cyclically fully commutative elements of Coxeter groups</a>, J. Algebr. Comb. 36, No. 1, 123-148 (2012), Table 1 type H.

%F a(n) = A000984(n) -2^(n+2) +n+3.

%F -finite: -(n+1)*(131*n-245) *a(n) +2*(563*n^2-867*n-245) *a(n-1) +3*(-1099*n^2+2480*n-1105) *a(n-2) +2*(1987*n^2-5829*n+4205) *a(n-3) -4*(209*n-178)*(2*n-5) *a(n-4)=0. - _R. J. Mathar_, Jun 11 2019

%p seq( binomial(2*n+2,n+1)-2^(n+2)+n+3,n=0..20);

%K nonn,easy

%O 0,2

%A _Ken Fan_