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A286072 Number of permutations of [n] where adjacent cycles differ in size.

%I A286072 #9 May 24 2018 02:56:32
%S A286072 1,1,1,5,16,84,512,3572,28080,256820,2553728,28064776,337319944,
%T A286072 4385615904,61255920936,921584068648,14720437293952,250190161426720,
%U A286072 4507229152534944,85630125536152160,1711040906290680448,35969941361999955392,790961860293623563648
%N A286072 Number of permutations of [n] where adjacent cycles differ in size.
%C A286072 Each cycle is written with the smallest element first and cycles are arranged in increasing order of their first elements.
%H A286072 Alois P. Heinz, <a href="/A286072/b286072.txt">Table of n, a(n) for n = 0..450</a>
%H A286072 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%p A286072 b:= proc(n, i) option remember; `if`(n=0, 1, add(`if`(i=j, 0,
%p A286072       (j-1)!*b(n-j, `if`(j>n-j, 0, j))*binomial(n-1, j-1)), j=1..n))
%p A286072     end:
%p A286072 a:= n-> b(n, 0):
%p A286072 seq(a(n), n=0..30);
%t A286072 b[n_, i_] := b[n, i] = If[n == 0, 1, Sum[If[i == j, 0, (j - 1)!*b[n - j, If[j > n - j, 0, j]]*Binomial[n - 1, j - 1]], {j, 1, n}]];
%t A286072 a[n_] := b[n, 0];
%t A286072 Table[a[n], {n, 0, 30}] (* _Jean-François Alcover_, May 24 2018, translated from Maple *)
%Y A286072 Cf. A275313, A286071, A286073, A286074, A286075, A286076, A286077.
%K A286072 nonn
%O A286072 0,4
%A A286072 _Alois P. Heinz_, May 01 2017