A322283 - OEIS

%I #22 Mar 29 2023 15:24:53

%S 1,1,1,1,1,1,1,1,1,1,2,22,242,2002,13442,77506,397826,1862146,8085506,

%T 32978946,127758774,482490294,2015041314,13111486674,144226353414,

%U 1835958708870,22030803357420,240151251989220,2389590181956120,21944411982069720,187919216043135720

%N Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 10).

%H Seiichi Manyama, <a href="/A322283/b322283.txt">Table of n, a(n) for n = 0..557</a>

%H David Galvin, John Engbers, and Clifford Smyth, <a href="https://arxiv.org/abs/2303.14057">Reciprocals of thinned exponential series</a>, arXiv:2303.14057 [math.CO], 2023.

%H Ira M. Gessel, <a href="https://arxiv.org/abs/1807.09290">Reciprocals of exponential polynomials and permutation enumeration</a>, arXiv:1807.09290 [math.CO], 2018.

%F E.g.f.: 1/(1 - x + x^2/2! - x^3/3! + x^4/4! - x^5/5! + x^6/6! - x^7/7! + x^8/8! - x^9/9!).

%t m = 31; CoefficientList[1/Normal[Exp[-x]+O[x]^10]+O[x]^m, x]*Range[0, m-1]! (* _Jean-François Alcover_, Feb 24 2019 *)

%o (PARI) N=40; x='x+O('x^N); Vec(serlaplace(1/sum(k=0, 9, (-x)^k/k!)))

%Y Cf. A000142, A322251 (mod 3), A317111 (mod 4), A322276 (mod 5), A322262 (mod 6), A322297 (mod 7), A322282 (mod 8), A322298 (mod 9).

%K nonn

%O 0,11

%A _Seiichi Manyama_, Dec 02 2018