A322298 -id:A322298 - cp's OEIS frontend

A322297 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 7).

1, 1, 1, 1, 1, 1, 1, 2, 16, 128, 800, 4160, 18944, 78080, 301160, 1208066, 6753606, 60823622, 648980646, 6581663766, 60475366230, 505780634070, 3921237755958, 29226687666930, 227116001463258, 2092153010685722, 24250743543656922, 322040690042341562

Offset: 0

Alois P. Heinz, Dec 02 2018

nonn

Alois P. Heinz, Table of n, a(n) for n = 0..526

Cf. A317111, A322251, A322262, A322276, A322298.

A322282 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 8).

Original entry on oeis.org

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

Offset: 0

Seiichi Manyama, Dec 02 2018

nonn

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

Cf. A000142, A322251 (mod 3), A317111 (mod 4), A322276 (mod 5), A322262 (mod 6), A322297 (mod 7), A322298 (mod 9), A322283 (mod 10).

m = 28; CoefficientList[1/Normal[Exp[-x]+O[x]^8]+O[x]^m, x]*Range[0, m-1]! (* Jean-François Alcover, Feb 24 2019 *)

N=40; x='x+O('x^N); Vec(serlaplace(1/sum(k=0, 7, (-x)^k/k!)))

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

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

Original entry on oeis.org

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

Seiichi Manyama, Dec 02 2018

nonn

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.

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

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

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

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!).

cp's OEIS Frontend

A322297 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 7).

Views

Author

Keywords

Links

Crossrefs

A322282 Number of permutations of [n] in which the length of every increasing run is 0 or 1 (mod 8).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

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

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula