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 A074881 Triangle T(n,k) giving number of labeled cyclic subgroups of order k in symmetric group S_n, n >= 1, 1 <= k <= g(n), where g(n) = A000793(n) is Landau's function. 4
 1, 1, 1, 1, 3, 1, 1, 9, 4, 3, 1, 25, 10, 15, 6, 10, 1, 75, 40, 90, 36, 120, 1, 231, 175, 420, 126, 735, 120, 126, 105, 1, 763, 616, 2730, 336, 5320, 960, 1260, 1008, 840, 336, 1, 2619, 2884, 15498, 756, 41580, 4320, 11340, 6720, 6804, 7560, 4320, 3024, 2268 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 COMMENTS A057731 contains zeros.  This sequence contains only positive values of A057731(n,k)/A000010(k). - Alois P. Heinz, Feb 16 2013 LINKS Alois P. Heinz, Rows n = 1..42, flattened FORMULA T(n,k) = A057731(n,k)/A000010(k). EXAMPLE Triangle begins: 1; 1,   1; 1,   3,   1; 1,   9,   4,   3; 1,  25,  10,  15,   6,  10; 1,  75,  40,  90,  36, 120; 1, 231, 175, 420, 126, 735, 120, 126, 105; MATHEMATICA nmax = 10; T[n_, k_] := n! SeriesCoefficient[O[x]^(n+1) + Sum[MoebiusMu[k/i]*Exp[ Sum[x^j/j, {j, Divisors[i]}]], {i, Divisors[k]}], {x, 0, n}]/ EulerPhi[k]; Table[DeleteCases[Table[T[n, k], {k, 1, 2 nmax}], 0], {n, 1, nmax}] // Flatten (* Jean-François Alcover, Sep 16 2019, after Andrew Howroyd *) PROG (PARI) T(n, k)={n!*polcoeff(sumdiv(k, i, moebius(k/i)*exp(sumdiv(i, j, x^j/j) + O(x*x^n))), n)/eulerphi(k)} \\ Andrew Howroyd, Jul 02 2018 CROSSREFS Row sums give A051625. Cf. A000010, A181949. Sequence in context: A069605 A080510 A124496 * A142992 A145905 A171435 Adjacent sequences:  A074878 A074879 A074880 * A074882 A074883 A074884 KEYWORD nonn,tabf AUTHOR Vladeta Jovovic, Sep 30 2002 STATUS approved

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Last modified May 29 03:06 EDT 2020. Contains 334696 sequences. (Running on oeis4.)