%I #5 Mar 23 2014 19:53:35

%S 1,0,1,0,1,3,0,2,10,15,0,6,40,105,105,0,24,196,700,1260,945,0,120,

%T 1148,5068,12600,17325,10395,0,720,7848,40740,126280,242550,270270,

%U 135135,0,5040,61416,363660,1332100,3213210,5045040,4729725,2027025,0,40320,541728,3584856,15020720,43022980,85345260,113513400,91891800,34459425

%N Triangle read by rows: T(0,0)=1; T(m,0)=0; otherwise T(m,n) = (m-1)*T(m-1,n)+(m-1+n)*T(m-1,n-1).

%C If the first column is omitted we get A075856, which has much more information about this triangle.

%D P. W. Shor, Problem 78-6: A combinatorial identity, in Problems and Solutions column, SIAM Review; problem in 20, p. 394 (1978); solution in 21, pp. 258-260 (1979).

%e Triangle begins:

%e 1,

%e 0, 1,

%e 0, 1, 3,

%e 0, 2, 10, 15,

%e 0, 6, 40, 105, 105,

%e 0, 24, 196, 700, 1260, 945,

%e 0, 120, 1148, 5068, 12600, 17325, 10395,

%e 0, 720, 7848, 40740, 126280, 242550, 270270, 135135,

%e ...

%p T:=proc(m,n) option remember;

%p if (m=0) and (n=0) then 1;

%p elif (m=0) or (n=0) then 0;

%p else (m-1)*T(m-1,n)+(m-1+n)*T(m-1,n-1); fi; end;

%p M:=20;

%p for m from 0 to M do

%p lprint([seq(T(m,n),n=0..m)]); od:

%Y Cf. A075856.

%K nonn,tabl

%O 0,6

%A _N. J. A. Sloane_, Mar 23 2014