%I A050447
%S A050447 1,1,1,1,2,1,1,3,3,1,1,4,6,5,1,1,5,10,14,8,1,1,6,15,30,31,13,1,1,7,21,
%T A050447 55,85,70,21,1,1,8,28,91,190,246,157,34,1,1,9,36,140,371,671,707,353,
%U A050447 55,1,1,10,45,204,658,1547,2353,2037,793,89,1,1,11,55,285,1086,3164
%N A050447 Table T(n,m) giving total degree of n-th-order elementary symmetric polynomials 
               in m variables, -1 <= n, 1 <= m, transposed and read by antidiagonals.
%D A050447 J. Berman and P. Koehler, Cardinalities of finite distributive lattices, 
               Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 
               103-124.
%D A050447 S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, 
               Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (see 
               p. 120).
%D A050447 Manfred Goebel, Rewriting Techniques and Degree Bounds for Higher Order 
               Symmetric Polynomials, Applicable Algebra in Engineering, Communication 
               and Computing (AAECC), Volume 9, Issue 6 (1999), 559-573.
%D A050447 G. Kreweras, Les preordres totaux compatibles avec un ordre partiel. 
               Math. Sci. Humaines No. 53 (1976), 5-30.
%F A050447 See PARI code. See A050446 for recurrence.
%e A050447 Table begins
%e A050447 1 1 1 1 1 1 1 ...
%e A050447 1 2 3 4 5 6 7 ...
%e A050447 1 3 6 10 15 21 28 ...
%e A050447 1 5 14 30 55 91 140 ...
%e A050447 1 8 31 85 190 371 658 ...
%o A050447 (PARI) M(n)=matrix(n,n,i,j,if(sign(i+j-n)-1,0,1)); V(n)=vector(n,i,1); 
               P(r,n)=vecmax(V(r)*M(r)^n) (from Benoit Cloitre, Jan 27, 2003. P(r,
               n) is T(n,k).)
%Y A050447 Rows give A000217, A000330, A006322, ..., columns give A000045, A006356, 
               A006357, A006358, ... Cf. A050446.
%Y A050447 Sequence in context: A073714 A144151 A022818 this_sequence A167172 A166293 
               A094525
%Y A050447 Adjacent sequences: A050444 A050445 A050446 this_sequence A050448 A050449 
               A050450
%K A050447 nonn,easy,nice,tabl
%O A050447 0,5
%A A050447 N. J. A. Sloane (njas(AT)research.att.com), Dec 23 1999
%E A050447 More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jul 03 
               2001