A250285 Number of permutations p of [n] such that p(i) > p(i+1) iff i == 0 (mod 8).

1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 44, 164, 494, 1286, 3002, 6434, 12869, 194464, 1925200, 12394480, 62224336, 261667792, 959874928, 3154435120, 9464040829, 210311057024, 3007458113984, 27514536974144, 193384741516784, 1123028832217904, 5617639404687824

Offset

0,10

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, 8)), j=1..u),
               add(b(u+j-1, o-j, irem(t+1, 8)), j=1..o)))
    end:
a:= n-> b(n, 0$2):
seq(a(n), n=0..35);

Mathematica

nmax = 30; CoefficientList[Series[1 + Sum[(x^(8 - k) * HypergeometricPFQ[{1}, {9/8 - k/8, 5/4 - k/8, 11/8 - k/8, 3/2 - k/8, 13/8 - k/8, 7/4 - k/8, 15/8 - k/8, 2 - k/8}, -x^8/16777216])/(8 - k)!, {k, 0, 7}] / HypergeometricPFQ[{}, {1/8, 1/4, 3/8, 1/2, 5/8, 3/4, 7/8}, -x^8/16777216], {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Apr 21 2021 *)

Crossrefs

Row n=8 of A181937.

Sequence in context: A252871 A307044 A165618 * A059596 A327386 A341386

Adjacent sequences: A250282 A250283 A250284 * A250286 A250287 A250288

Keyword

nonn

Author

Alois P. Heinz, Nov 16 2014

Status

approved