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A345342 Number of permutations of [2n] having n 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
1, 1, 11, 195, 5033, 171465, 7264499, 368258891, 21740278417, 1465044247953, 110975742044635, 9334724676616339, 863320991981279033, 87072657503374176985, 9511213780859395685955, 1118615909510940858978075, 140933163945864346869845025, 18937018020284359019138011425 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..332

Wikipedia, Permutation

FORMULA

a(n) = A344855(2n,n).

a(n) ~ c * (1 + exp(2))^n * (n-1)!, where c = 0.1823720711148962856100934464088354177502714116352616187167... - Vaclav Kotesovec, Jul 15 2021

MAPLE

b:= proc(n) option remember; `if`(n=0, 1, add(expand(x*

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

    end:

a:= n-> coeff(b(2*n), x, n):

seq(a(n), n=0..18);

MATHEMATICA

b[n_] := b[n] = If[n == 0, 1, Sum[Expand[x b[n-j] Binomial[n-1, j-1]* Ceiling[2^(j-2)]], {j, n}]];

a[n_] := Coefficient[b[2n], x, n];

Table[a[n], {n, 0, 18}] (* Jean-Fran├žois Alcover, Aug 25 2021, after Alois P. Heinz *)

CROSSREFS

Cf. A344855.

Sequence in context: A112127 A142996 A201185 * A218818 A243646 A186251

Adjacent sequences:  A345339 A345340 A345341 * A345343 A345344 A345345

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Jun 14 2021

STATUS

approved

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Last modified October 21 05:06 EDT 2021. Contains 348141 sequences. (Running on oeis4.)