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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. 1
1, 1, 5, 5887172299, 1025638889935309161425800069552344, 11337715575060644543768059040620852798601554512475786008052416860406653219312996 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..5.

FORMULA

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))).

a(n) asymptotic to n^(n^3)/(n!^4).

CROSSREFS

Cf. A091058, A091510.

Sequence in context: A052000 A094467 A242828 * A177164 A067483 A186685

Adjacent sequences:  A091508 A091509 A091510 * A091512 A091513 A091514

KEYWORD

nonn

AUTHOR

Christian G. Bower, Jan 16 2004

STATUS

approved

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Last modified November 22 16:20 EST 2014. Contains 249807 sequences.