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Triangle T(n,k) represents the coefficients of (x^20*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.
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%I #5 Mar 23 2013 15:02:52

%S 1,20,1,780,60,1,45240,4320,120,1,3483480,382200,13800,200,1,

%T 334414080,40556880,1734600,33600,300,1,38457619200,5039012160,

%U 243505080,5699400,69300,420,1

%N Triangle T(n,k) represents the coefficients of (x^20*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

%e 1;

%e 20,1;

%e 780,60,1;

%e 45240,4320,120,1;

%e 3483480,382200,13800,200,1;

%e 334414080,40556880,1734600,33600,300,1;

%e 38457619200,5039012160,243505080,5699400,69300,420,1;

%e 5153320972800,718724260800,38155703040,1024322880,15262800,127680,560,1;

%p b[0]:=f(x):

%p for j from 1 to 10 do

%p b[j]:=simplify(x^20*diff(b[j-1],x$1);

%p end do;

%Y Cf. A008277, A019538, A035342, A035469, A049029, A049385, A092082, A132056, A223511-A223522, A223168-A223172, A223523-A223532.

%K nonn,easy,tabl

%O 1,2

%A _Udita Katugampola_, Mar 23 2013