|
| |
|
|
A068026
|
|
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=9.
|
|
2
|
|
|
|
1, 1023, 29524, 698027, 2441406, 36192156, 47079208, 408345795, 653757313, 2773708938, 2593742460, 26912354924, 11488207654, 51851591352, 77226922344, 222984027123, 125999618778, 848125888467, 340614792100, 1991478050562
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,2
|
|
|
LINKS
|
|
|
|
FORMULA
|
1/9!*(sigma[1](n)^9 + 36*sigma[1](n)^7*sigma[2](n) + 168*sigma[1](n)^6*sigma[3](n) + 378*sigma[1](n)^5*sigma[2](n)^2 + 756*sigma[1](n)^5*sigma[4](n) + 2520*sigma[1](n)^4*sigma[2](n)*sigma[3](n) +
+ 1260*sigma[1](n)^3*sigma[2](n)^3 + 3024*sigma[1](n)^4*sigma[5](n) + 7560*sigma[1](n)^3*sigma[2](n)*sigma[4](n) + 3360*sigma[1](n)^3*sigma[3](n)^2 + 7560*sigma[1](n)^2*sigma[2](n)^2*sigma[3](n) +
+ 945*sigma[1](n)*sigma[2](n)^4 + 10080*sigma[1](n)^3*sigma[6](n) + 18144*sigma[1](n)^2*sigma[2](n)*sigma[5](n) + 15120*sigma[1](n)^2*sigma[3](n)*sigma[4](n) + 11340*sigma[1](n)*sigma[2](n)^2*sigma[4](n) + 10080*sigma[1](n)*sigma[2](n)*sigma[3](n)^2 + 2520*sigma[2](n)^3*sigma[3](n) + 25920*sigma[7](n)*sigma[1](n)^2 +
+ 30240*sigma[1](n)*sigma[2](n)*sigma[6](n) + 24192*sigma[1](n)*sigma[3](n)*sigma[5](n) + 11340*sigma[1](n)*sigma[4](n)^2 + 9072*sigma[2](n)^2*sigma[5](n) + 15120*sigma[2](n)*sigma[3](n)*sigma[4](n) + 2240*sigma[3](n)^3 + 25920*sigma[7](n)*sigma[2](n) + 45360*sigma[8](n)*sigma[1](n) + 20160*sigma[3](n)*sigma[6](n) + 18144*sigma[4](n)*sigma[5](n) + 40320*sigma[9](n)).
|
|
|
MATHEMATICA
|
CIP9 = CycleIndexPolynomial[SymmetricGroup[9], Array[x, 9]]; a[n_] := CIP9 /. x[k_] -> DivisorSigma[k, n]; Array[a, 20] (* Jean-François Alcover, Nov 04 2016 *)
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
