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%I #7 Mar 31 2012 10:23:14
%S 1,2,1,6,6,1,12,36,12,1,40,180,120,20,1,60,960,1020,300,30,1,378,4620,
%T 8400,3780,630,42,1,-336,24864,65520,44240,10920,1176,56,1,8496,
%U 114912,512568,488880,171360,26712,2016,72,1,-51120,679680,3885840,5261760
%N Triangle T(n,m) = coefficient of x^n in expansion of [x*(x+1)^(x+1)]^m = sum(n>=m, T(n,m) x^n*m!/n!).
%F T(n,m):=(n)!/(m)!*sum(k=0..n-m, k!*sum(i=k..n-m, (stirling1(i,k)*binomial(k,n-i-m))/i!)*m^k/k!).
%e 1
%e 2, 1,
%e 6, 6, 1,
%e 12, 36, 12, 1,
%e 40, 180, 120, 20, 1,
%e 60, 960, 1020, 300, 30, 1,
%e 378, 4620, 8400, 3780, 630, 42, 1
%o (Maxima)
%o T(n,m):=(n)!/(m)!*sum(k!*sum((stirling1(i,k)*binomial(k,n-i-m))/i!,i,k,n-m)*m^k/k!,k,0,n-m);
%K sign,tabl
%O 1,2
%A _Vladimir Kruchinin_, Dec 14 2011
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