cp's OEIS Frontend

A082424 Coefficient of s(2n) in s(n,n) * s(n,n) * s(n,n) * s(n,n) * s(n,n) * s(n,n), where s(n,n) is the Schur function indexed by two parts of size n, s(2n) is the Schur function corresponding to the trivial representation and * represents the inner or Kronecker product.

%I A082424 #4 Sep 22 2013 15:58:09
%S A082424 1,1,11,41,320,1917,14582,100562,688427,4380888,26324611,148136566,
%T A082424 785175771,3925637781,18586683128,83578440418,358079558873,
%U A082424 1465784048253,5748270468573,21649265291143,78483868584001
%N A082424 Coefficient of s(2n) in s(n,n) * s(n,n) * s(n,n) * s(n,n) * s(n,n) * s(n,n), where s(n,n) is the Schur function indexed by two parts of size n, s(2n) is the Schur function corresponding to the trivial representation and * represents the inner or Kronecker product.
%D A082424 I. G. Macdonald, Symmetric Functions and Hall Polynomials, Oxford Mathematical Monographs, Oxford Univ. Press, second edition, 1995.
%F A082424 a(n) = Sum_{gamma} Chi^{(n, n)}( gamma )^6/z(gamma) the sum is over all partitions gamma of 2n Chi^lambda(gamma) is the value of the symmetric group character z(gamma) is the size of the stablizer of the conjugacy class of symmetric group indexed by the partition gamma
%p A082424 compsclr := proc(k) local gamma; add( combinat[Chi]( [k,k], gamma)^6/ZEE(gamma),gamma= combinat[partition](2*k)); end: ZEE := proc (mu) local res, m, i; m := 1; res := convert(mu,`*`); for i from 2 to nops(mu) do if mu[i] <> mu[i-1] then m := 1 else m := m+1 fi; res := res*m; od; res; end:
%Y A082424 Cf. A008763 change 6 to 4 in the above program.
%K A082424 nonn
%O A082424 0,3
%A A082424 _Mike Zabrocki_, Apr 24 2003