A223517 Triangle T(n,k) represents the coefficients of (x^15*d/dx)^n, where n=1,2,3,...; generalization of Stirling numbers of second kind A008277, Lah-numbers A008297.

1, 15, 1, 435, 45, 1, 18705, 2415, 90, 1, 1066185, 158775, 7725, 150, 1, 75699135, 12497985, 722700, 18825, 225, 1, 6434426475, 1150525845, 75372885, 2379300, 38850, 315, 1, 637008221025, 121487010975, 8763187230, 318061485, 6380850, 71610, 420, 1

Offset: 1

Author

Udita Katugampola, Mar 23 2013

Keywords

• nonn
• easy
• tabl

Examples

			1;
15,1;
435,45,1;
18705,2415,90,1;
1066185,158775,7725,150,1;
75699135,12497985,722700,18825,225,1;
6434426475,1150525845,75372885,2379300,38850,315,1;
637008221025,121487010975,8763187230,318061485,6380850,71610,420,1;
		

Crossrefs

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

Programs

Maple

b[0]:=f(x):
for j from 1 to 10 do
b[j]:=simplify(x^15*diff(b[j-1],x$1);
end do;