|
%I #12 Mar 31 2012 10:23:14
%S 1,0,1,0,0,1,24,0,0,1,-60,120,0,0,1,240,-360,360,0,0,1,1260,1680,
%T -1260,840,0,0,1,-12096,30240,6720,-3360,1680,0,0,1,105840,-290304,
%U 226800,20160,-7560,3024,0,0,1,-388800,2721600,-2358720,1058400,50400,-15120
%N Triangle T(n,m) = coefficient of x^n in expansion of x^m*(x+1)^(m*x^2) = sum(n>=m, T(n,m) x^n*m!/n!).
%C 1
%F T(n,m):=n!/m!*sum(k=0..(n-m)/2, (m^k*stirling1(n-m-2*k,k))/(n-m-2*k)!).
%e 1,
%e 0, 1,
%e 0, 0, 1,
%e 24, 0, 0, 1,
%e -60, 120, 0, 0, 1,
%e 240, -360, 360, 0, 0, 1,
%e 1260, 1680, -1260, 840, 0, 0, 1
%o (Maxima)
%o T(n,m):=n!/m!*sum((m^k*stirling1(n-m-2*k,k))/(n-m-2*k)!,k,0,(n-m)/2);
%K sign,tabl
%O 1,7
%A _Vladimir Kruchinin_, Dec 13 2011
|
