A322282 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 8).

1, 1, 1, 1, 1, 1, 1, 1, 2, 18, 162, 1122, 6402, 31746, 141570, 580866, 2241096, 8693256, 43232904, 362491272, 4067218584, 45304757784, 459941563224, 4236342378840, 35804034476496, 281634733757520, 2106753678778320, 15739783039815120

Offset

0,9

Links

Seiichi Manyama, Table of n, a(n) for n = 0..537

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! + x^6/6! - x^7/7!).

Mathematica

m = 28; CoefficientList[1/Normal[Exp[-x]+O[x]^8]+O[x]^m, x]*Range[0, m-1]! (* Jean-François Alcover, Feb 24 2019 *)

Prog

(PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/sum(k=0, 7, (-x)^k/k!)))

Crossrefs

Cf. A000142, A322251 (mod 3), A317111 (mod 4), A322276 (mod 5), A322262 (mod 6), A322297 (mod 7), A322298 (mod 9), A322283 (mod 10).

Sequence in context: A052876 A121933 A108550 * A270369 A352654 A144513

Adjacent sequences: A322279 A322280 A322281 * A322283 A322284 A322285

Keyword

nonn

Author

Seiichi Manyama, Dec 02 2018

Status

approved