|
|
A262166
|
|
Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 4.
|
|
4
|
|
|
1, 1, 2, 5, 20, 86, 516, 3135, 25080, 196468, 1964680, 18827225, 225926700, 2559350288, 35830904032, 468385940355, 7494175045680, 111029569712844, 1998532254831192, 33092842524631733, 661856850492634660, 12113055891685809704, 266487229617087813488
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
|
|
MAPLE
|
b:= proc(u, o, c) option remember; `if`(c<0 or c>4, 0, `if`(u+o=0,
x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..4))(add(
b(u-j, o-1+j, c-1), j=1..u)+add(b(u+j-1, o-j, c+1), j=1..o))))
end:
a:= n-> (p-> add(coeff(p, x, i), i=0..min(n, 4)))(b(0, n, 0)):
seq(a(n), n=0..25);
|
|
MATHEMATICA
|
b[u_, o_, c_] := b[u, o, c] = If[c < 0 || c > 4, 0, If[u + o == 0, x^c, Function[p, Sum[Coefficient[p, x, i]*x^Max[i, c], {i, 0, 4}]][Sum[b[u - j, o - 1 + j, c - 1], {j, u}] + Sum[b[u + j - 1, o - j, c + 1], {j, o}]]]];
a[n_] := Function[p, Sum[Coefficient[p, x, i], {i, 0, Min[n, 4]}]][b[0, n, 0]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|