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 A242027 Number T(n,k) of endofunctions on [n] with cycles of k distinct lengths; triangle T(n,k), n>=0, 0<=k<=A003056(n), read by rows. 14
 1, 0, 1, 0, 4, 0, 24, 3, 0, 206, 50, 0, 2300, 825, 0, 31742, 14794, 120, 0, 522466, 294987, 6090, 0, 9996478, 6547946, 232792, 0, 218088504, 160994565, 8337420, 0, 5344652492, 4355845868, 299350440, 151200, 0, 145386399554, 128831993037, 11074483860, 18794160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Rows n = 0..140, flattened EXAMPLE T(3,2) = 3: (1,3,2), (3,2,1), (2,1,3). Triangle T(n,k) begins: 00 :  1; 01 :  0,          1; 02 :  0,          4; 03 :  0,         24,          3; 04 :  0,        206,         50; 05 :  0,       2300,        825; 06 :  0,      31742,      14794,       120; 07 :  0,     522466,     294987,      6090; 08 :  0,    9996478,    6547946,    232792; 09 :  0,  218088504,  160994565,   8337420; 10 :  0, 5344652492, 4355845868, 299350440, 151200; MAPLE with(combinat): b:= proc(n, i, k) option remember; `if`(n=0, `if`(k=0, 1, 0),       `if`(i<1 or k<1, 0, add((i-1)!^j*multinomial(n, n-i*j, i\$j)/j!*       b(n-i*j, i-1, k-`if`(j=0, 0, 1)), j=0..n/i)))     end: T:= (n, k)-> add(binomial(n-1, j-1)*n^(n-j)*b(j\$2, k), j=0..n): seq(seq(T(n, k), k=0..floor((sqrt(1+8*n)-1)/2)), n=0..14); MATHEMATICA multinomial[n_, k_] := n!/Times @@ (k!); b[n_, i_, k_] := b[n, i, k] = If[n == 0, If[k==0, 1, 0], If[i<1 || k<1, 0, Sum[(i-1)!^j*multinomial[n, Join[ {n-i*j}, Array[i&, j]]]/j!*b[n-i*j, i-1, k-If[j==0, 0, 1]], {j, 0, n/i}]] ]; T[0, 0] = 1; T[n_, k_] := Sum[Binomial[n-1, j-1]*n^(n-j)*b[j, j, k], {j, 0, n}]; Table[T[n, k], {n, 0, 14}, {k, 0, Floor[(Sqrt[1+8n]-1)/2]}] // Flatten (* Jean-François Alcover, Feb 18 2017, translated from Maple *) CROSSREFS Columns k=0-10 give: A000007, A241980 for n>0, A246283, A246284, A246285, A246286, A246287, A246288, A246289, A246290, A246291. Row sums give A000312. T(A000217(n),n) gives A246292. Cf. A003056, A060281, A218868 (the same for permutations). Sequence in context: A229827 A295839 A243270 * A329891 A057402 A269214 Adjacent sequences:  A242024 A242025 A242026 * A242028 A242029 A242030 KEYWORD nonn,tabf AUTHOR Alois P. Heinz, Aug 11 2014 STATUS approved

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Last modified June 16 19:05 EDT 2021. Contains 345068 sequences. (Running on oeis4.)