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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. 1

%I

%S 1,1,10,1074,1637124,45156692400,27230193578558160,

%T 420296434943941609215120,190200071567439616748736269178720,

%U 2843464512159537301384360263178682136716160,1562137388408002436396705025296003247844758163480828800

%N 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 R. H. Hardin, <a href="/A190945/b190945.txt">Table of n, a(n) for n = 1..13</a>

%e All solutions for n=3

%e ..3....3....3....3....3....2....1....3....3....2

%e ..2....1....2....2....2....3....3....1....2....3

%e ..3....3....1....3....3....2....2....2....3....1

%e ..2....2....3....1....2....3....3....3....1....3

%e ..1....3....2....2....3....1....2....2....3....2

%e ..3....2....3....3....1....3....3....3....2....3

%o (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 nonn

%O 1,3

%A _R. H. Hardin_ May 24 2011

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