%I A059098
%S A059098 1,1,1,2,3,2,5,10,12,6,15,37,62,60,24,52,151,320,450,360,120,203,674,
%T A059098 1712,3120,3720,2520,720,877,3263,9604,21336,33600,34440,20160,5040,
%U A059098 4140,17007,56674,147756,287784,394800,352800,181440,40320,21147,94828
%N A059098 Triangle T(n,m)=Sum_{i=0..n} stirling2(n,i)*Product_{j=1..m} (i-j+1), 
               m=0..n.
%C A059098 T(n,0)=A000110; T(n,1)=A005493. Row sums give A059099.
%F A059098 E.g.f. for T(n, m): (e^x-1)^m*(e^(e^x-1)).
%e A059098 [1], [1, 1], [2, 3, 2], [5, 10, 12, 6], [15, 37, 62, 60, 24], [52, 151, 
               320, 450, 360, 120], ...; E.g.f. for T(n, 2) = (e^x-1)^2*(e^(e^x-1)) 
               = x^2 + 2*x^3 + 31/12*x^4 + 8/3*x^5 + 107/45*x^6 + 343/180*x^7 + 
               28337/20160*x^8 + 349/360*x^9 + ...; E.g.f. for T(n, 3) = (e^x-1)^3*(e^(e^x-1)) 
               = x^3 + 5/2*x^4 + 15/4*x^5 + 13/3*x^6 + 127/30*x^7 + 1759/480*x^8 
               + 34961/12096*x^9 + ...
%Y A059098 Cf. A049020, A001861, A059099.
%Y A059098 Sequence in context: A079535 A050159 A147294 this_sequence A082050 A162687 
               A010242
%Y A059098 Adjacent sequences: A059095 A059096 A059097 this_sequence A059099 A059100 
               A059101
%K A059098 easy,nonn,tabl
%O A059098 0,4
%A A059098 Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 02 2001