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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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10
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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.
a(n) = A000302(n) - A181765(n).
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REFERENCES
| 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
| T. D. Noe, Table of n, a(n) for n=0..200
S. R. Finch, Signum equations and extremal coefficients.
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FORMULA
| Sum of squares of coefficients in Product_{k=1..n} (1+x^k):
a(n) = Sum_{k=0..n(n+1)/2} A053632(n,k)^2. [From Paul D. Hanna (pauldhanna(AT)juno.com), Nov 30 2010]
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MAPLE
| f:=n->coeff( expand( mul((x^k+1/x^k)^2, k=1..n) ), x, 0);
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PROG
| (PARI) a(n)=polcoeff(prod(k=-n, n, 1+x^k), 0)/2
(PARI) {a(n)=sum(k=0, n*(n+1)/2, polcoeff(prod(m=1, n, 1+x^m+x*O(x^k)), k)^2)} [From Paul D. Hanna]
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CROSSREFS
| a(n)=A000980(n)/2. Cf. A025591.
Cf. A053632; variant: A127728.
Sequence in context: A007578 A007580 A000085 * A148100 A149815 A149816
Adjacent sequences: A047650 A047651 A047652 * A047654 A047655 A047656
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Michael Somos, Jun 10, 2000.
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