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A322262 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 6). 7
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,7
LINKS
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
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Dec 01 2018
STATUS
approved

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Last modified February 27 15:09 EST 2024. Contains 370376 sequences. (Running on oeis4.)