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 A261430 Number A(n,k) of permutations p of [n] without fixed points such that p^k = Id; square array A(n,k), n>=0, k>=0, read by antidiagonals. 10
 1, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 9, 0, 15, 0, 0, 1, 0, 0, 2, 0, 0, 40, 0, 0, 0, 1, 0, 1, 0, 3, 24, 105, 0, 105, 0, 0, 1, 0, 0, 0, 0, 20, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 9, 0, 175, 0, 2625, 2240, 945, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,25 LINKS Alois P. Heinz, Antidiagonals n = 0..140, flattened FORMULA E.g.f. of column k: exp(Sum_{d|k, d>1} x^d/d). EXAMPLE Square array A(n,k) begins:   1, 1,   1,  1,    1,  1,    1,   1,    1, ...   0, 0,   0,  0,    0,  0,    0,   0,    0, ...   0, 0,   1,  0,    1,  0,    1,   0,    1, ...   0, 0,   0,  2,    0,  0,    2,   0,    0, ...   0, 0,   3,  0,    9,  0,    3,   0,    9, ...   0, 0,   0,  0,    0, 24,   20,   0,    0, ...   0, 0,  15, 40,  105,  0,  175,   0,  105, ...   0, 0,   0,  0,    0,  0,  210, 720,    0, ...   0, 0, 105,  0, 2625,  0, 4585,   0, 7665, ... MAPLE with(numtheory): A:= proc(n, k) option remember; `if`(n<0, 0, `if`(n=0, 1,       add(mul(n-i, i=1..j-1)*A(n-j, k), j=divisors(k) minus {1})))     end: seq(seq(A(n, d-n), n=0..d), d=0..14); MATHEMATICA A[0, 0] = A[0, 1] = 1; A[_, 0|1] = 0; A[n_, k_] := A[n, k] = If[n < 0, 0, If[n == 0, 1, Sum[Product[n - i, {i, 1, j - 1}]*A[n - j, k], {j, Rest @ Divisors[k]}]]]; Table[A[n, d - n], {d, 0, 14}, {n, 0, d}] // Flatten (* Jean-François Alcover, Jan 21 2017, after Alois P. Heinz *) CROSSREFS Columns k=0+1,2-10 give: A000007, A001147, A052502, A052503, A052504, A261317, A261427, A261428, A261429, A261381. Main diagonal gives A261431. Cf. A008307. Sequence in context: A097946 A083926 A218757 * A024466 A021817 A069585 Adjacent sequences:  A261427 A261428 A261429 * A261431 A261432 A261433 KEYWORD nonn,tabl AUTHOR Alois P. Heinz, Aug 18 2015 STATUS approved

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Last modified February 27 18:47 EST 2020. Contains 332308 sequences. (Running on oeis4.)