A202184 - OEIS

%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