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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.)