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A190945 Number of permutations of the n*(n+1)/2 numbers (i copies of i | i=1..n), with no element equal to another within a distance of 1.

%I A190945 #29 Jan 12 2025 17:17:27
%S A190945 1,1,10,1074,1637124,45156692400,27230193578558160,
%T A190945 420296434943941609215120,190200071567439616748736269178720,
%U A190945 2843464512159537301384360263178682136716160,1562137388408002436396705025296003247844758163480828800
%N A190945 Number of permutations of the n*(n+1)/2 numbers (i copies of i | i=1..n), with no element equal to another within a distance of 1.
%H A190945 Seiichi Manyama, <a href="/A190945/b190945.txt">Table of n, a(n) for n = 1..36</a> (a(1)-a(13) from R. H. Hardin).
%e A190945 All solutions for n=3
%e A190945 ..3....3....3....3....3....2....1....3....3....2
%e A190945 ..2....1....2....2....2....3....3....1....2....3
%e A190945 ..3....3....1....3....3....2....2....2....3....1
%e A190945 ..2....2....3....1....2....3....3....3....1....3
%e A190945 ..1....3....2....2....3....1....2....2....3....2
%e A190945 ..3....2....3....3....1....3....3....3....2....3
%o A190945 (Maxima) a(n):=sum(p!*coeff(expand(product(sum(binomial(k-1,k-j)*(-1)^(k-j)* (t^j/j!),j,1,k),k,1,n)),t,p),p,n,n*(n+1)/2); /* _Tani Akinari_, Sep 15 2012 */
%K A190945 nonn
%O A190945 1,3
%A A190945 _R. H. Hardin_, May 24 2011