OFFSET
0,12
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
MathOverflow, Why 'excedances' of permutations? [closed].
EXAMPLE
Triangle begins:
1
0 1
1 0 1
1 1 1 1
1 3 1 2 1
2 3 4 3 3 1
3 4 8 6 6 4 1
4 7 12 13 12 10 5 1
5 13 16 26 24 22 15 6 1
7 19 27 43 48 46 37 21 7 1
10 26 47 68 90 93 83 58 28 8 1
For example, row n = 6 counts the following compositions:
(6) (15) (114) (123) (1113) (11112) (111111)
(24) (42) (132) (1311) (1122) (11121)
(33) (51) (141) (2112) (1131) (11211)
(231) (213) (2121) (1212) (12111)
(222) (2211) (1221)
(312) (3111) (21111)
(321)
(411)
MATHEMATICA
pw[y_]:=Length[Select[Range[Length[y]], #>=y[[#]]&]];
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], pw[#]==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); [Vecrev(p) | p<-r]}
{ 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
STATUS
approved