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

0,11

Links

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

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 *)

Crossrefs

Row n=9 of A181937.

Sequence in context: A223927 A307045 A035927 * A289254 A059597 A327387

Adjacent sequences: A250283 A250284 A250285 * A250287 A250288 A250289

Keyword

nonn

Author

Alois P. Heinz, Nov 16 2014

Status

approved