OFFSET
0,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (1 - 2*x + 5*x^2 + 2*x^3 + 10*x^4 + 12*x^5 + 32*x^6 + 20*x^7 + 56*x^8 + 20*x^9 + 32*x^10 + 12*x^11 + 10*x^12 + 2*x^13 + 5*x^14 - 2*x^15 + x^16)/((1 - x)^12*(1 + x)^4*(1 + x^2)^2*(1 + x + x^2)^4). - Andrew Howroyd, Apr 18 2021
MATHEMATICA
Needs["Combinatorica`"]; n = 4; nn = 25; CoefficientList[Series[PairGroupIndex[SymmetricGroup[n], s] /.Table[s[i] -> 1/(1 - x^i)^2, {i, 1, Binomial[n, 2]}], {x, 0, nn}], x]
PROG
(PARI)
permcount(v) = {my(m=1, s=0, k=0, t); for(i=1, #v, t=v[i]; k=if(i>1&&t==v[i-1], k+1, 1); m*=t*k; s+=t); s!/m}
edges(v, t) = {prod(i=2, #v, prod(j=1, i-1, my(g=gcd(v[i], v[j])); t(v[i]*v[j]/g)^g )) * prod(i=1, #v, my(c=v[i]); t(c)^((c-1)\2)*if(c%2, 1, t(c/2)))}
G(n)={my(s=0); forpart(p=n, s+=permcount(p)/edges(p, i->(1-x^i)^2)); s/n!}
{ Vec(G(4) + O(x^36)) } \\ Andrew Howroyd, Apr 18 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Aug 10 2015
EXTENSIONS
Terms a(26) and beyond from Andrew Howroyd, Apr 18 2021
STATUS
approved