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A286075 Number of permutations of [n] with increasing cycle sizes.

%I A286075 #7 May 28 2018 09:19:56
%S A286075 1,1,1,3,8,38,182,1194,7932,69192,591936,6286272,66914880,840036960,
%T A286075 10567285920,154755036000,2246755924800,37283584936320,
%U A286075 618705247829760,11472473012232960,212762383625594880,4386435706887413760,89954629722500659200,2030764767987849062400
%N A286075 Number of permutations of [n] with increasing cycle sizes.
%C A286075 Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
%H A286075 Alois P. Heinz, <a href="/A286075/b286075.txt">Table of n, a(n) for n = 0..450</a>
%H A286075 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A286075 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i>n, 0,
%p A286075       b(n, i+1)+b(n-i, i+1)*(i-1)!*binomial(n-1, i-1)))
%p A286075     end:
%p A286075 a:= n-> b(n, 1):
%p A286075 seq(a(n), n=0..30);
%t A286075 b[n_, i_] := b[n, i] = If[n == 0, 1, If[i > n, 0, b[n, i + 1] + b[n - i, i + 1]*(i - 1)!*Binomial[n - 1, i - 1]]];
%t A286075 a[n_] := b[n, 1];
%t A286075 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 28 2018, from Maple *)
%Y A286075 Cf. A275312, A286071, A286072, A286073, A286074, A286076, A286077.
%K A286075 nonn
%O A286075 0,4
%A A286075 _Alois P. Heinz_, May 01 2017