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

Author

Seiichi Manyama, Dec 01 2018

Keywords

• nonn

Examples

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

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.

Crossrefs

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

Programs

PARI

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

Formula

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