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A320978 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of four. 2
0, 1, 5, 123, 778, 14126, 111811, 1957924, 18846572, 342736488, 3904186779, 75626480215, 996651530998, 20739117286767, 310506509296055, 6952893022274589, 116561453850733664, 2805243168612301480, 52046467944203248643, 1342921799608903158968 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..455

FORMULA

a(n) = A262129(n) - A262128(n).

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-> coeff(add(b(j-1, n-j, 0), j=1..n), x, 4):

seq(a(n), n=4..30);

CROSSREFS

Column k=4 of A262125.

Cf. A262128, A262129.

Sequence in context: A267914 A282882 A208394 * A196425 A193612 A195949

Adjacent sequences:  A320975 A320976 A320977 * A320979 A320980 A320981

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 25 2018

STATUS

approved

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Last modified January 25 14:40 EST 2022. Contains 350572 sequences. (Running on oeis4.)