OFFSET
0,5
COMMENTS
Triangle T(n,k), 0 <= k <= n, read by rows, given by [1, 0, 1, 0, 1, 0, 1, 0, 1, ...] DELTA [1, 2, 3, 4, 5, 6, 7, 8, 9, ...] where DELTA is the operator defined in A084938.
T(n,k), 0 <= k <= n, is the number of elements in the Coxeter group B_n with absolute length k. - Jose Bastidas, Jul 14 2023
LINKS
Seiichi Manyama, Rows n = 0..139, flattened
FORMULA
T(n,m) = T(n-1,m) + (2*n-1)*T(n-1,m-1) with T(n,n) = (2*n-1)!! and T(n,0) = 1. - Johannes W. Meijer, Jun 08 2009
EXAMPLE
Triangle T(n,k) begins:
1;
1, 1;
1, 4, 3;
1, 9, 23, 15;
1, 16, 86, 176, 105;
1, 25, 230, 950, 1689, 945;
1, 36, 505, 3480, 12139, 19524, 10395;
...
MAPLE
nmax:=8; mmax:=nmax: for n from 0 to nmax do a(n, n) := doublefactorial(2*n-1) od: for n from 0 to nmax do a(n, 0):=1 od: for n from 2 to nmax do for m from 1 to n-1 do a(n, m) := a(n-1, m) + (2*n-1)*a(n-1, m-1) od; od: seq(seq(a(n, m), m=0..n), n=0..nmax); # Johannes W. Meijer, Jun 08 2009, revised Nov 25 2012
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Philippe Deléham, Aug 08 2005
STATUS
approved