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A320981 Number of permutations p of [n] such that the up-down signature of p has nonnegative partial sums with a maximal value of seven. 2
0, 1, 8, 1031, 9379, 486299, 5084162, 196352061, 2352460536, 81070646577, 1103813259377, 36592927821767, 560827842703887, 18549898652794829, 317078625531545481, 10667284286197389079, 201655098112826170280, 6973904694490809821089, 144705018721890264334923 (list; graph; refs; listen; history; text; internal format)
OFFSET

7,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 7..452

FORMULA

a(n) = A262132(n) - A262131(n).

MAPLE

b:= proc(u, o, c) option remember; `if`(c<0 or c>7, 0, `if`(u+o=0,

       x^c, (p-> add(coeff(p, x, i)*x^max(i, c), i=0..7))(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, 7):

seq(a(n), n=7..30);

CROSSREFS

Column k=7 of A262125.

Cf. A262131, A262132.

Sequence in context: A122067 A076688 A004808 * A316395 A176372 A047943

Adjacent sequences:  A320978 A320979 A320980 * A320982 A320983 A320984

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 25 2018

STATUS

approved

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Last modified May 25 22:51 EDT 2022. Contains 354073 sequences. (Running on oeis4.)