A322283 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 10).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 22, 242, 2002, 13442, 77506, 397826, 1862146, 8085506, 32978946, 127758774, 482490294, 2015041314, 13111486674, 144226353414, 1835958708870, 22030803357420, 240151251989220, 2389590181956120, 21944411982069720, 187919216043135720

Offset

0,11

Links

Seiichi Manyama, Table of n, a(n) for n = 0..557

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! + x^8/8! - x^9/9!).

Mathematica

m = 31; CoefficientList[1/Normal[Exp[-x]+O[x]^10]+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, 9, (-x)^k/k!)))

Crossrefs

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

Sequence in context: A086855 A089182 A138140 * A151617 A334603 A342232

Adjacent sequences: A322280 A322281 A322282 * A322284 A322285 A322286

Keyword

nonn

Author

Seiichi Manyama, Dec 02 2018

Status

approved