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A218868 Triangular array read by rows: T(n,k) is the number of n-permutations that have exactly k distinct cycle lengths. 8
1, 2, 3, 3, 10, 14, 25, 95, 176, 424, 120, 721, 3269, 1050, 6406, 21202, 12712, 42561, 178443, 141876, 436402, 1622798, 1418400, 151200, 3628801, 17064179, 17061660, 2162160, 48073796, 177093256, 212254548, 41580000, 479001601, 2293658861, 2735287698, 719072640 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

T(A000217(n),n) gives A246292. - Alois P. Heinz, Aug 21 2014

LINKS

Alois P. Heinz, Rows n = 1..170, flattened

P. Flajolet and R. Sedgewick, Analytic Combinatorics, Cambridge University Press, 2009

FORMULA

E.g.f.: Product_{i>=1} (1 + y*exp(x^i/i) - y).

EXAMPLE

:      1;

:      2;

:      3,       3;

:     10,      14;

:     25,      95;

:    176,     424,     120;

:    721,    3269,    1050;

:   6406,   21202,   12712;

:  42561,  178443,  141876;

: 436402, 1622798, 1418400, 151200;

MAPLE

with(combinat):

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

      `if`(i<1, 0, add((i-1)!^j*multinomial(n, n-i*j, i$j)/j!*

      b(n-i*j, i-1)*`if`(j=0, 1, x), j=0..n/i))))

    end:

T:= n-> (p-> seq(coeff(p, x, i), i=1..degree(p)))(b(n$2)):

seq(T(n), n=1..16);  # Alois P. Heinz, Aug 21 2014

MATHEMATICA

nn=10; a=Product[1-y+y Exp[x^i/i], {i, 1, nn}]; f[list_]:=Select[list, #>0&]; Map[f, Drop[Range[0, nn]!CoefficientList[Series[a , {x, 0, nn}], {x, y}], 1]]//Grid

CROSSREFS

Columns k=1-3 give: A005225, A005772, A133119.

Row sums are: A000142.

Row lengths are: A003056.

Cf. A208437, A242027 (the same for endofunctions), A246292, A317327.

Sequence in context: A123027 A100652 A094416 * A329874 A152300 A117030

Adjacent sequences:  A218865 A218866 A218867 * A218869 A218870 A218871

KEYWORD

nonn,tabf

AUTHOR

Geoffrey Critzer, Nov 07 2012

STATUS

approved

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Last modified December 8 01:46 EST 2019. Contains 329850 sequences. (Running on oeis4.)