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 A322384 Number T(n,k) of entries in the k-th cycles of all permutations of [n] when cycles are ordered by decreasing lengths (and increasing smallest elements); triangle T(n,k), n>=1, 1<=k<=n, read by rows. 5
 1, 3, 1, 13, 4, 1, 67, 21, 7, 1, 411, 131, 46, 11, 1, 2911, 950, 341, 101, 16, 1, 23563, 7694, 2871, 932, 197, 22, 1, 213543, 70343, 26797, 9185, 2311, 351, 29, 1, 2149927, 709015, 275353, 98317, 27568, 5119, 583, 37, 1, 23759791, 7867174, 3090544, 1141614, 343909, 73639, 10366, 916, 46, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Alois P. Heinz, Rows n = 1..50, flattened Wikipedia, Permutation EXAMPLE The 6 permutations of {1,2,3} are:   (1)     (2) (3)   (1,2)   (3)   (1,3)   (2)   (2,3)   (1)   (1,2,3)   (1,3,2) so there are 13 elements in the first cycles, 4 in the second cycles and only 1 in the third cycles. Triangle T(n,k) begins:        1;        3,     1;       13,     4,     1;       67,    21,     7,    1;      411,   131,    46,   11,    1;     2911,   950,   341,  101,   16,   1;    23563,  7694,  2871,  932,  197,  22,  1;   213543, 70343, 26797, 9185, 2311, 351, 29, 1; MAPLE b:= proc(n, l) option remember; `if`(n=0, add(l[-i]*       x^i, i=1..nops(l)), add(binomial(n-1, j-1)*       b(n-j, sort([l[], j]))*(j-1)!, j=1..n))     end: T:= n-> (p-> (seq(coeff(p, x, i), i=1..n)))(b(n, [])): seq(T(n), n=1..12); CROSSREFS Column k=1 gives A028418. Row sums give A001563. Cf. A185105, A322383. Sequence in context: A295827 A277197 A297898 * A113139 A266577 A143411 Adjacent sequences:  A322381 A322382 A322383 * A322385 A322386 A322387 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Dec 05 2018 STATUS approved

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Last modified October 17 06:08 EDT 2019. Contains 328106 sequences. (Running on oeis4.)