A322262 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 6).

1, 1, 1, 1, 1, 1, 2, 14, 98, 546, 2562, 10626, 41118, 174174, 1093092, 10005996, 98041944, 889104216, 7315812504, 55893493656, 421564046904, 3519008733240, 36011379484080, 435775334314320, 5538098453968080, 68428271204813520, 805379194188288720

Offset

0,7

Links

Seiichi Manyama, Table of n, a(n) for n = 0..514

David Galvin, John Engbers, and Clifford Smyth, Reciprocals of thinned exponential series, arXiv:2303.14057 [math.CO], 2023.

Ira M. Gessel, Reciprocals of exponential polynomials and permutation enumeration, arXiv:1807.09290 [math.CO], 2018.

Formula

E.g.f.: 1/(1 - x + x^2/2! - x^3/3! + x^4/4! - x^5/5!).

Example

For n=6 the a(6)=2 permutations are 654321 and 123456.

Prog

(PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/sum(k=0, 5, (-x)^k/k!)))

Crossrefs

Cf. A000142, A322251 (mod 3), A317111 (mod 4), A322276 (mod 5).

Sequence in context: A267913 A204699 A286445 * A109808 A304444 A247481

Adjacent sequences: A322259 A322260 A322261 * A322263 A322264 A322265

Keyword

nonn

Author

Seiichi Manyama, Dec 01 2018

Status

approved