%I A050446
%S A050446 1,1,1,1,2,1,1,3,3,1,1,5,6,4,1,1,8,14,10,5,1,1,13,31,30,15,6,1,1,21,70,
%T A050446 85,55,21,7,1,1,34,157,246,190,91,28,8,1,1,55,353,707,671,371,140,36,9,
%U A050446 1,1,89,793,2037,2353,1547,658,204,45,10,1,1,144,1782,5864,8272
%N A050446 Table T(n,m) giving total degree of n-th-order elementary symmetric polynomials 
               in m variables, -1 <= n, 1 <= m, read by antidiagonals.
%C A050446 T(n,m) is a polynomial of degree n in m. For example, T(2,m)=(m+1)(m+2)/
               2. For the polynomials corresponding to n=1,2,...,10, see the Cyvin-Gutman 
               reference (p. 143). Kekule numbers for certain benzenoids. - Emeric 
               Deutsch (deutsch(AT)duke.poly.edu), Jun 12 2005
%D A050446 J. Berman and P. Koehler, Cardinalities of finite distributive lattices, 
               Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 
               103-124.
%D A050446 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 A050446 S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, 
               Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (pp. 
               142-144).
%F A050446 T(n, m) = T(n, m-1) + Sum( T(2k, m-1)*T(n-1-2k, m), {k, 0, (n-1)/2})
%e A050446 Table begins
%e A050446 1 1 1 1 1 1 1 ...
%e A050446 1 2 3 4 5 6 7 ...
%e A050446 1 3 6 10 15 21 28 ...
%e A050446 1 5 14 30 55 91 140 ...
%e A050446 1 8 31 85 190 371 658 ...
%Y A050446 Rows give A000217, A000330, A006322, ..., columns give A000045, A006356, 
               A006357, A006358, ... Cf. A050447.
%Y A050446 Cf. A050447.
%Y A050446 Sequence in context: A138201 A154221 A026736 this_sequence A144048 A113983 
               A089980
%Y A050446 Adjacent sequences: A050443 A050444 A050445 this_sequence A050447 A050448 
               A050449
%K A050446 nonn,easy,nice,tabl
%O A050446 0,5
%A A050446 N. J. A. Sloane (njas(AT)research.att.com), Dec 23 1999
%E A050446 More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jul 03 
               2001