A286071 - OEIS

%I #11 May 24 2018 02:56:25

%S 1,1,2,5,19,85,496,3229,25117,215225,2100430,22187281,261228199,

%T 3284651245,45163266604,659277401525,10380194835601,172251467909809,

%U 3057368096689690,56867779157145769,1122474190194034555,23137433884903034501,502874858021076645784

%N Number of permutations of [n] with nonincreasing cycle sizes.

%C Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.

%C a(n) is even if and only if n in { A016825 }.

%H Alois P. Heinz, <a href="/A286071/b286071.txt">Table of n, a(n) for n = 0..450</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>

%e a(3) = 5: (123), (132), (12)(3), (13)(2), (1)(2)(3).

%e a(4) = 19: (1234), (1243), (1324), (1342), (1423), (1432), (123)(4), (132)(4), (124)(3), (142)(3), (12)(34), (12)(3)(4), (134)(2), (143)(2), (13)(24), (13)(2)(4), (14)(23), (14)(2)(3), (1)(2)(3)(4).

%p b:= proc(n, i) option remember; `if`(n=0, 1, add((j-1)!*

%p       b(n-j, j)*binomial(n-1, j-1), j=1..min(n, i)))

%p     end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..30);

%t b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[(j - 1)!*b[n - j, j]*Binomial[n - 1, j - 1], {j, 1, Min[n, i]}]];

%t a[n_] := b[n, n];

%t Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 24 2018, translated from Maple *)

%Y Cf. A016825, A275310, A286072, A286073, A286074, A286075, A286076, A286077.

%K nonn

%O 0,3

%A _Alois P. Heinz_, May 01 2017