%I A091511
%S A091511 1,1,5,5887172299,1025638889935309161425800069552344,
%T A091511 11337715575060644543768059040620852798601554512475786008052416860406653219312996
%N A091511 Number of n X n X n 3-D matrices over symbol set {1,...,n} equivalent 
               under any permutation of rows, columns, stacks or the symbol set.
%F A091511 a(n) = sum {1*s_1+2*s_2+...=n, 1*t_1+2*t_2+...=n, 1*u_1+2*u_2+...=n, 
               1*v_1+2*v_2+...=n} (fix A[s_1, s_2, ...;t_1, t_2, ...;u_1, u_2, ...;
               v_1, v_2, ...]/(1^s_1*s_1!*2^s_2*s_2!*...*1^t_1*t_1!*2^t_2*t_2!*...*1^u_1*u_1!*2^u_2*u_2!*...*1^v_1*v_1!*\
               2^v_2*v_2!*...)) where fix A[...] = prod {i, j, k>=1} ( (sum {d|lcm(i, 
               j, k)} (d*v_d))^(s_i*t_j*u_k*lcm(i, j, k)/(i*j*k)))
%F A091511 a(n) asymptotic to n^(n^3)/(n!^4)
%Y A091511 Cf. A091058, A091510.
%Y A091511 Sequence in context: A115763 A052000 A094467 this_sequence A067483 A102638 
               A005872
%Y A091511 Adjacent sequences: A091508 A091509 A091510 this_sequence A091512 A091513 
               A091514
%K A091511 nonn
%O A091511 0,3
%A A091511 Christian G. Bower (bowerc(AT)usa.net), Jan 16 2004