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A091057 Number of n X n matrices over symbol set {1,...,n^2} equivalent under any permutation of row, columns or the symbol set. 9
1, 1, 9, 777, 18500104, 322286625959257, 7368376339801908226685191, 422262377369187686156418513093399998333, 105882936532098986759153041871810253870024776751177723954 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..8.

C. G. Bower, Explanation of A091057-A091062

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} (fix A[s_1, s_2, ...;t_1, t_2, ...;u_1, u_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!*...)) where fix A[...] = prod {i, j>=1} ( (sum {d|lcm(i, j)} (d*u_d))^(gcd(i, j)*s_i*t_j)).

CROSSREFS

Cf. A091058-A091062, A242095.

Row sums of A242106.

Sequence in context: A223380 A246125 A246126 * A168257 A303143 A137065

Adjacent sequences:  A091054 A091055 A091056 * A091058 A091059 A091060

KEYWORD

nonn

AUTHOR

Christian G. Bower, Dec 17 2003

EXTENSIONS

a(7), a(8) from Max Alekseyev, Feb 09 2010

STATUS

approved

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Last modified October 21 15:18 EDT 2021. Contains 348155 sequences. (Running on oeis4.)