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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
0, 1, 3, 11, 48, 238, 1318, 8054, 53728, 387836, 3007940, 24917668, 219375104, 2043792680, 20074003368, 207186660712, 2240632127232, 25324980662544, 298471543286448, 3660469596095280, 46627358889945344, 615855211031451104, 8421273619742748256 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..527

Wikipedia, Permutation

FORMULA

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

MAPLE

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

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

    end:

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

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

MATHEMATICA

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

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

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

Table[a[n], {n, 0, 23}] (* Jean-Fran├žois Alcover, Aug 25 2021, after Alois P. Heinz *)

CROSSREFS

Cf. A344855.

Sequence in context: A316703 A192399 A233162 * A186185 A317170 A127087

Adjacent sequences:  A345338 A345339 A345340 * A345342 A345343 A345344

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 14 2021

STATUS

approved

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Last modified September 28 09:32 EDT 2021. Contains 347714 sequences. (Running on oeis4.)