OFFSET
0,7
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325
MathOverflow, Why 'excedances' of permutations? [closed].
EXAMPLE
Triangle begins:
1
1 0
1 1 0
2 1 1 0
3 2 2 1 0
4 5 3 3 1 0
6 8 7 6 4 1 0
9 12 15 12 10 5 1 0
13 19 27 25 22 15 6 1 0
18 32 43 51 46 37 21 7 1 0
25 51 70 94 94 83 58 28 8 1 0
For example, row n = 6 counts the following compositions (empty column indicated by dot):
(6) (51) (312) (1113) (11112) (111111) .
(15) (114) (411) (1122) (11121)
(24) (132) (1131) (2112) (11211)
(33) (141) (1212) (2121) (21111)
(42) (213) (1221) (3111)
(123) (222) (1311) (12111)
(231) (2211)
(321)
MATHEMATICA
pa[y_]:=Length[Select[Range[Length[y]], #>y[[#]]&]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], pa[#]==k&]], {n, 0, 15}, {k, 0, n}]
PROG
(PARI) T(n)={my(v=vector(n+1, i, i==1), r=v); for(k=1, n, v=vector(#v, j, sum(i=1, j-1, if(k>i, x, 1)*v[j-i])); r+=v); vector(#v, i, Vecrev(r[i], i))}
{ my(A=T(10)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Jan 19 2023
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Mar 22 2022
EXTENSIONS
Terms a(66) and beyond from Andrew Howroyd, Jan 19 2023
STATUS
approved