A223515 - OEIS

A223515

Triangle T(n,k) represents the coefficients of (x^13*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

%I #5 Mar 23 2013 14:55:06

%S 1,13,1,325,39,1,12025,1807,78,1,589225,102375,5785,130,1,35942725,

%T 6936475,466830,14105,195,1,2623818925,549241875,41948725,1538810,

%U 29120,273,1,223024608625,49858620175,4198780950,177364005,4130490,53690,364,1,21633387036625

%N Triangle T(n,k) represents the coefficients of (x^13*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

%e 1;

%e 13,1;

%e 325,39,1;

%e 12025,1807,78,1;

%e 589225,102375,5785,130,1;

%e 35942725,6936475,466830,14105,195,1

%e 2623818925,549241875,41948725,1538810,29120,273,1;

%e 223024608625,49858620175,4198780950,177364005,4130490,53690,364,1;

%e 21633387036625,...

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

%p for j from 1 to 10 do

%p b[j]:=simplify(x^13*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