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A345341 Total number of cycles in all permutations of [n] having cycles of the form (c1, c2, ..., c_m) where c1 = min_{i>=1} c_i and c_j = min_{i>=j} c_i or c_j = max_{i>=j} c_i. 2

%I

%S 0,1,3,11,48,238,1318,8054,53728,387836,3007940,24917668,219375104,

%T 2043792680,20074003368,207186660712,2240632127232,25324980662544,

%U 298471543286448,3660469596095280,46627358889945344,615855211031451104,8421273619742748256

%N Total number of cycles in all permutations of [n] having cycles of the form (c1, c2, ..., c_m) where c1 = min_{i>=1} c_i and c_j = min_{i>=j} c_i or c_j = max_{i>=j} c_i.

%H Alois P. Heinz, <a href="/A345341/b345341.txt">Table of n, a(n) for n = 0..527</a>

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

%F a(n) = Sum_{k=1..n} k * A344855(n,k).

%p b:= proc(n) option remember; `if`(n=0, [1, 0], add((p-> p+[0,

%p p[1]])(b(n-j)*binomial(n-1, j-1)*ceil(2^(j-2))), j=1..n))

%p end:

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

%p seq(a(n), n=0..23);

%t b[n_] := b[n] = If[n == 0, {1, 0}, Sum[Function[p, p + {0,

%t p[[1]]}][b[n-j] Binomial[n-1, j-1] Ceiling[2^(j-2)]], {j, 1, n}]];

%t a[n_] := b[n][[2]];

%t Table[a[n], {n, 0, 23}] (* _Jean-Fran├žois Alcover_, Aug 25 2021, after _Alois P. Heinz_ *)

%Y Cf. A344855.

%K nonn

%O 0,3

%A _Alois P. Heinz_, Jun 14 2021

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Last modified October 22 18:11 EDT 2021. Contains 348175 sequences. (Running on oeis4.)