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Number of arrangements of n 1's, n 2's, ..., n n's avoiding equal consecutive terms.
3

%I #26 May 27 2019 18:06:42

%S 1,1,2,174,2265024,7946203275000,12229789732207993835280,

%T 12202002913678756821228939869239920,

%U 10937192762438008527903830198163831816546577931520,11655577382287102750765311537460065620507094071664576111302628243840

%N Number of arrangements of n 1's, n 2's, ..., n n's avoiding equal consecutive terms.

%H Seiichi Manyama, <a href="/A321634/b321634.txt">Table of n, a(n) for n = 0..26</a>

%H Mathematics.StackExchange, <a href="https://math.stackexchange.com/questions/129451/find-the-number-of-arrangements-of-k-mbox-1s-k-mbox-2s-cdots">Find the number of k 1's, k 2's, ... , k n's - total kn cards</a>, Apr 08 2012.

%F a(n) ~ n^(n^2 - n/2 + 1) / ((2*Pi)^((n-1)/2) * exp(n - 5/12)). - _Vaclav Kotesovec_, Nov 24 2018

%o (PARI) {a(n) = sum(i=n, n^2, i!*polcoef(sum(j=1, n, (-1)^(n-j)*binomial(n-1, j-1)*x^j/j!)^n, i))} \\ _Seiichi Manyama_, May 27 2019

%Y Cf. A000142, A110706, A114938, A193638, A321633, A321666.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 15 2018