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a(n) = (6*n^2)!/((n^2)!^6).
0

%I #13 Jan 30 2023 14:06:02

%S 1,720,3246670537110000,101097362223624462291180422369532000000,

%T 11820969246826954556547676599863670334721199951925900837836206749590000

%N a(n) = (6*n^2)!/((n^2)!^6).

%C For n >= 1, a(n) is the number of possible combinations of an n X n X n Rubik's cube with randomly placed stickers.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Rubik&#39;s_Cube">Rubik's Cube</a>.

%F a(n) = (6*n^2)!/((n^2)!^6).

%t Table[(6*n^2)!/(n^2)!^6, {n, 0, 4}]

%o (Magma) [Factorial(6*n^2)/Factorial(n^2)^6: n in [0..4]];

%o (PARI) a(n)=(6*n^2)!/(n^2)!^6;

%Y Cf. A201555.

%K nonn,easy

%O 0,2

%A _Arkadiusz Wesolowski_, Feb 27 2017