A068024 Z(S_m; sigma[1](n), sigma[2](n),..., sigma[m](n)) where Z(S_m; x_1,x_2,...,x_m) is the cycle index of the symmetric group S_m and sigma[k](n) is the sum of k-th powers of divisors of n; m=7.

1, 255, 3280, 43435, 97656, 998184, 960800, 6347715, 8069620, 27615060, 21435888, 184770040, 67977560, 263540112, 343123440, 866251507, 435984840, 2595218340, 943531280, 4944199260, 3308659904, 5722701624, 3559590240

Offset

1,2

Links

Table of n, a(n) for n=1..23.

Formula

1/7!*(sigma[1](n)^7 + 21*sigma[1](n)^5*sigma[2](n) + 70*sigma[1](n)^4*sigma[3](n) + 105*sigma[1](n)^3*sigma[2](n)^2 + 210*sigma[1](n)^3*sigma[4](n) + 420*sigma[1](n)^2*sigma[2](n)*sigma[3](n) + 105*sigma[1](n)*sigma[2](n)^3 + 504*sigma[1](n)^2*sigma[5](n) + 630*sigma[1](n)*sigma[2](n)*sigma[4](n) + 280*sigma[1](n)*sigma[3](n)^2 + 210*sigma[2](n)^2*sigma[3](n) + 840*sigma[1](n)*sigma[6](n) + 504*sigma[2](n)*sigma[5](n) + 420*sigma[3](n)*sigma[4](n) + 720*sigma[7](n)).

Mathematica

CIP7 = CycleIndexPolynomial[SymmetricGroup[7], Array[x, 7]]; a[n_] := CIP7 /. x[k_] -> DivisorSigma[k, n]; Array[a, 23] (* Jean-François Alcover, Nov 04 2016 *)

Crossrefs

Cf. A067692, A068020-A068023, A068025-A068027, A000203, A001157-A001160, A013954, A013955.

Sequence in context: A206048 A160908 A038995 * A028524 A075940 A075945

Adjacent sequences: A068021 A068022 A068023 * A068025 A068026 A068027

Keyword

nonn

Author

Vladeta Jovovic, Feb 08 2002

Status

approved