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

0,9

Links

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

Example

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

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 *)

Crossrefs

Row n=7 of A181937.

Sequence in context: A307041 A325732 A124090 * A328019 A327243 A059595

Adjacent sequences: A250281 A250282 A250283 * A250285 A250286 A250287

Keyword

nonn

Author

Alois P. Heinz, Nov 16 2014

Status

approved