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A322282 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 8). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

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

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-Fran├žois 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 A144513 A037518

Adjacent sequences:  A322279 A322280 A322281 * A322283 A322284 A322285

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Dec 02 2018

STATUS

approved

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Last modified December 15 03:48 EST 2019. Contains 329990 sequences. (Running on oeis4.)