%I A055858
%S A055858 1,1,2,4,9,6,27,64,48,36,256,625,500,400,320,3125,7776,6480,5400,4500,
%T A055858 3750,46656,117649,100842,86436,74088,63504,54432,823543,2097152,
%U A055858 1835008,1605632,1404928,1229312,1075648,941192,16777216,43046721
%N A055858 Coefficient triangle for certain polynomials.
%C A055858 The coefficients of the partner polynomials are found in triangle A055864.
%F A055858 a(n, m)=0 if n<m; a(0, 0)=1, a(n, 0)= n^n, n >= 1, a(n, m)= n^(m-1)*(n+1)^(n-m+1), 
               n >= m >= 1;
%F A055858 E.g.f. for column m: A(m, x); A(0, x)= 1/(1+W(-x)); A(1, x)= -1-diff(W(-x), 
               x) = -1-W(-x)/((1+W(-x))*x); A(2, x)=A(1, x)-int(A(1, x), x)/x-(1/
               x+x); recursion: A(m, x) = A(m-1, x)-int(A(m-1, x), x)/x-((m-1)^(m-1))*(x^(m-1))/
               (m-1)!, m >= 3; W(x) principal branch of Lambert's function.
%e A055858 {1}; {1,2}; {4,9,6}; {27,64,48,36};...
%e A055858 Fourth row polynomial (n=3): p(3,x)= 27+64*x+48*x^2+36*x^3
%Y A055858 Column sequences are A000312(n), n >= 1, A055860 (A000169), A055861 (A053506), 
               A055862-3 for m=0..4, row sums: A045531(n+1)= |A039621(n+1, 2)|, 
               n >= 0.
%Y A055858 Sequence in context: A104654 A011182 A063507 this_sequence A141389 A133757 
               A076125
%Y A055858 Adjacent sequences: A055855 A055856 A055857 this_sequence A055859 A055860 
               A055861
%K A055858 easy,nonn,tabl
%O A055858 0,3
%A A055858 Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jun 20 
               2000