A321666 - OEIS

%I #27 Nov 10 2024 21:46:32

%S 1,1,1,29,94376,66218360625,16985819072511102549,

%T 2421032324142610480402567434373,

%U 271259741131895052775392614041761701799270286,32119646666355552112999645991677870426882424139287301894021793

%N Number of arrangements of n 1's, n 2's, ..., n n's avoiding equal consecutive terms and introduced in ascending order.

%H Seiichi Manyama, <a href="/A321666/b321666.txt">Table of n, a(n) for n = 0..27</a>

%F a(n) = A321634(n)/n!.

%F a(n) ~ exp(5/12) * n^((n-1)*(2*n-1)/2) / (2*Pi)^(n/2). - _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))/n!} \\ _Seiichi Manyama_, May 27 2019

%Y Main diagonal of A322013.

%Y Cf. A190826, A190830, A190833, A190835, A190836, A190837, A278990, A321634.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Nov 16 2018