[go: up one dir, main page]

login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A262171
Number of permutations p of [n] such that the up-down signature of 0,p has nonnegative partial sums with a maximal value <= 9.
4
1, 1, 2, 5, 20, 87, 522, 3271, 26168, 214955, 2149549, 21881092, 262569097, 3191307394, 44674222343, 631473609984, 10100709895340, 162823295801791, 2928983654856296, 53036572897985517, 1059539775650223369, 21293220263695186990, 467627502721031824736
OFFSET
0,3
LINKS
FORMULA
a(n) = A262163(n,9).
MAPLE
b:= proc(u, o, c) option remember; `if`(c<0 or c>9, 0, `if`(u+o=0,
x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..9))(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, 9)))(b(0, n, 0)):
seq(a(n), n=0..25);
CROSSREFS
Column k=9 of A262163.
Sequence in context: A262168 A262169 A262170 * A262172 A258830 A002484
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 13 2015
STATUS
approved