A250286 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 0 (mod 9).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 9, 54, 219, 714, 2001, 5004, 11439, 24309, 48619, 831384, 9069651, 64369341, 355150566, 1635163542, 6542615421, 23369110326, 75953123676, 227864057851, 5742168041637, 90830731860000, 920922875075934, 7159714782188364

Offset: 0

Author

Alois P. Heinz, Nov 16 2014

Keywords

• nonn

Links

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

Crossrefs

Row n=9 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, 9)), j=1..u),
               add(b(u+j-1, o-j, irem(t+1, 9)), j=1..o)))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..35);

Mathematica

nmax = 30; CoefficientList[Series[1 + Sum[(x^(9 - k) * HypergeometricPFQ[{1}, {10/9 - k/9, 11/9 - k/9, 4/3 - k/9, 13/9 - k/9, 14/9 - k/9, 5/3 - k/9, 16/9 - k/9, 17/9 - k/9, 2 - k/9}, -x^9/387420489])/(9 - k)!, {k, 0, 8}] / HypergeometricPFQ[{}, {1/9, 2/9, 1/3, 4/9, 5/9, 2/3, 7/9, 8/9}, -x^9/387420489], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 21 2021 *)