cp's OEIS Frontend

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.

%I A345341 #13 Aug 25 2021 05:28:08
%S A345341 0,1,3,11,48,238,1318,8054,53728,387836,3007940,24917668,219375104,
%T A345341 2043792680,20074003368,207186660712,2240632127232,25324980662544,
%U A345341 298471543286448,3660469596095280,46627358889945344,615855211031451104,8421273619742748256
%N 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.
%H A345341 Alois P. Heinz, <a href="/A345341/b345341.txt">Table of n, a(n) for n = 0..527</a>
%H A345341 Wikipedia, <a href="https://en.wikipedia.org/wiki/Permutation">Permutation</a>
%F A345341 a(n) = Sum_{k=1..n} k * A344855(n,k).
%p A345341 b:= proc(n) option remember; `if`(n=0, [1, 0], add((p-> p+[0,
%p A345341       p[1]])(b(n-j)*binomial(n-1, j-1)*ceil(2^(j-2))), j=1..n))
%p A345341     end:
%p A345341 a:= n-> b(n)[2]:
%p A345341 seq(a(n), n=0..23);
%t A345341 b[n_] := b[n] = If[n == 0, {1, 0}, Sum[Function[p, p + {0,
%t A345341     p[[1]]}][b[n-j] Binomial[n-1, j-1] Ceiling[2^(j-2)]], {j, 1, n}]];
%t A345341 a[n_] := b[n][[2]];
%t A345341 Table[a[n], {n, 0, 23}] (* _Jean-François Alcover_, Aug 25 2021, after _Alois P. Heinz_ *)
%Y A345341 Cf. A344855.
%K A345341 nonn
%O A345341 0,3
%A A345341 _Alois P. Heinz_, Jun 14 2021