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Search: id:A050446
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| A050446 |
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Table T(n,m) giving total degree of n-th-order elementary symmetric polynomials in m variables, -1 <= n, 1 <= m, read by antidiagonals. |
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| 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, 85, 55, 21, 7, 1, 1, 34, 157, 246, 190, 91, 28, 8, 1, 1, 55, 353, 707, 671, 371, 140, 36, 9, 1, 1, 89, 793, 2037, 2353, 1547, 658, 204, 45, 10, 1, 1, 144, 1782, 5864, 8272
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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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
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REFERENCES
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J. Berman and P. Koehler, Cardinalities of finite distributive lattices, Mitteilungen aus dem Mathematischen Seminar Giessen, 121 (1976), 103-124.
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.
S. J. Cyvin and I. Gutman, Kekule structures in benzenoid hydrocarbons, Lecture Notes in Chemistry, No. 46, Springer, New York, 1988 (pp. 142-144).
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FORMULA
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T(n, m) = T(n, m-1) + Sum( T(2k, m-1)*T(n-1-2k, m), {k, 0, (n-1)/2})
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EXAMPLE
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Table begins
1 1 1 1 1 1 1 ...
1 2 3 4 5 6 7 ...
1 3 6 10 15 21 28 ...
1 5 14 30 55 91 140 ...
1 8 31 85 190 371 658 ...
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CROSSREFS
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Rows give A000217, A000330, A006322, ..., columns give A000045, A006356, A006357, A006358, ... Cf. A050447.
Cf. A050447.
Sequence in context: A138201 A154221 A026736 this_sequence A144048 A113983 A089980
Adjacent sequences: A050443 A050444 A050445 this_sequence A050447 A050448 A050449
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KEYWORD
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nonn,easy,nice,tabl
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Dec 23 1999
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EXTENSIONS
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More terms from Naohiro Nomoto (6284968128(AT)geocities.co.jp), Jul 03 2001
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