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Search: id:A047653
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| A047653 |
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Constant term in expansion of (1/2) * Prod_{k=-n..n} 1+x^k. |
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+0
7
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| 1, 2, 4, 10, 26, 76, 236, 760, 2522, 8556, 29504, 103130, 364548, 1300820, 4679472, 16952162, 61790442, 226451036, 833918840, 3084255128, 11451630044, 42669225172, 159497648600, 597950875256, 2247724108772, 8470205600640
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OFFSET
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0,2
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COMMENT
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Or, constant term in expansion of Prod_{k=1..n} (x^k+1/x^k)^2. - N. J. A. Sloane (njas(AT)research.att.com), Jul 09 2008
Or, maximal coefficient of the polynomial (1+x)^2 * (1+x^2)^2 *...* (1+x^n)^2.
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REFERENCES
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R. P. Stanley, Weyl groups, the hard Lefschetz theorem and the Sperner property, SIAM J. Algebraic and Discrete Methods 1 (1980), 168-184.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..200
S. R. Finch, Signum equations and extremal coefficients.
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MAPLE
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f:=n->coeff( expand( mul((x^k+1/x^k)^2, k=1..n) ), x, 0);
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PROGRAM
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(PARI) a(n)=polcoeff(prod(k=-n, n, 1+x^k), 0)/2
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CROSSREFS
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a(n)=A000980(n)/2. Cf. A025591.
Sequence in context: A007578 A007580 A000085 this_sequence A148100 A149815 A149816
Adjacent sequences: A047650 A047651 A047652 this_sequence A047654 A047655 A047656
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Michael Somos, Jun 10, 2000.
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