OFFSET
0,3
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..2489 (rows 0..200)
MathOverflow, Why 'excedances' of permutations? [closed].
EXAMPLE
Triangle begins:
1
1
2
3 1
5 3
8 8
14 17 1
25 35 4
46 70 12
87 137 32
167 268 76 1
324 525 170 5
For example, row n = 6 counts the following compositions:
(6) (15) (123)
(51) (24)
(312) (33)
(411) (42)
(1113) (114)
(1122) (132)
(2112) (141)
(2121) (213)
(3111) (222)
(11112) (231)
(11121) (321)
(11211) (1131)
(21111) (1212)
(111111) (1221)
(1311)
(2211)
(12111)
MATHEMATICA
pdw[y_]:=Length[Select[Range[Length[y]], #<=y[[#]]&]];
DeleteCases[Table[Length[Select[Join@@ Permutations/@IntegerPartitions[n], pdw[#]==k&]], {n, 0, 10}, {k, 0, n}], 0, {2}]
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); r[1]=x; [Vecrev(p) | p<-r/x]}
{ my(A=T(10)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Jan 19 2023
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Mar 22 2022
STATUS
approved