cp's OEIS Frontend

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.

%I A068024 #7 Nov 04 2016 09:53:52
%S A068024 1,255,3280,43435,97656,998184,960800,6347715,8069620,27615060,
%T A068024 21435888,184770040,67977560,263540112,343123440,866251507,435984840,
%U A068024 2595218340,943531280,4944199260,3308659904,5722701624,3559590240
%N 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.
%F A068024 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)).
%t A068024 CIP7 = CycleIndexPolynomial[SymmetricGroup[7], Array[x, 7]]; a[n_] := CIP7 /. x[k_] -> DivisorSigma[k, n]; Array[a, 23] (* _Jean-François Alcover_, Nov 04 2016 *)
%Y A068024 Cf. A067692, A068020-A068023, A068025-A068027, A000203, A001157-A001160, A013954, A013955.
%K A068024 nonn
%O A068024 1,2
%A A068024 _Vladeta Jovovic_, Feb 08 2002