

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
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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, m1]! (* JeanFrançois 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



