A250284 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 0 (mod 7).

1, 1, 1, 1, 1, 1, 1, 1, 7, 35, 119, 329, 791, 1715, 3431, 45031, 400281, 2313633, 10467037, 39845281, 132908041, 398840401, 7677528495, 98103087719, 800524248391, 5030038213949, 26202586666879, 117991927960739, 472105349529479, 11979440405949527

Offset: 0

Author

Alois P. Heinz, Nov 16 2014

Keywords

• nonn

Examples

			a(7) = 1: 1234567.
a(8) = 7: 12345687, 12345786, 12346785, 12356784, 12456783, 13456782, 23456781.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..500

Crossrefs

Row n=7 of A181937.

Programs

Maple

b:= proc(u, o, t) option remember; `if`(u+o=0, 1,
     `if`(t=0, add(b(u-j, o+j-1, irem(t+1, 7)), j=1..u),
               add(b(u+j-1, o-j, irem(t+1, 7)), j=1..o)))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..35);

Mathematica

nmax = 30; CoefficientList[Series[1 + Sum[(x^(7 - k) * HypergeometricPFQ[{1}, {8/7 - k/7, 9/7 - k/7, 10/7 - k/7, 11/7 - k/7, 12/7 - k/7, 13/7 - k/7, 2 - k/7}, -x^7/823543])/(7 - k)!, {k, 0, 6}] / HypergeometricPFQ[{}, {1/7, 2/7, 3/7, 4/7, 5/7, 6/7}, -x^7/823543], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 21 2021 *)