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A096713
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Triangle of nonzero coefficients of the modified Hermite polynomials.
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2
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1, 1, -1, 1, -3, 1, 3, -6, 1, 15, -10, 1, -15, 45, -15, 1, -105, 105, -21, 1, 105, -420, 210, -28, 1, 945, -1260, 378, -36, 1, -945, 4725, -3150, 630, -45, 1, -10395, 17325, -6930, 990, -55, 1, 10395, -62370, 51975, -13860, 1485, -66, 1, 135135, -270270, 135135, -25740, 2145, -78
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OFFSET
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0,5
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COMMENTS
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Triangle of nonzero coefficients of matching polynomial of complete graph of order n.
Row sums of absolute values produce A000085 (number of involutions). - Wouter Meeussen, Mar 12 2008
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REFERENCES
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C. D. Godsil, Algebraic Combinatorics, Chapman & Hall, New York, 1993.
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LINKS
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Table of n, a(n) for n=0..54.
Eric Weisstein's World of Mathematics, Hermite Polynomial
Eric Weisstein's World of Mathematics, Matching Polynomial [From Eric W. Weisstein, Sep 27 2008]
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FORMULA
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HermiteH[n,x/Sqrt[2] ]/2^(n/2) - Wouter Meeussen, Mar 12 2008
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EXAMPLE
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1, x, -1 + x^2, -3*x + x^3, 3 - 6*x^2 + x^4, 15*x - 10*x^3 + x^5, ...
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MATHEMATICA
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Table[CoefficientList[HermiteH[n, x/Sqrt[2] ]/2^(n/2), x], {n, 0, 25}] - Wouter Meeussen, Mar 12 2008
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PROG
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(PARI) T(n, k)=if(k<0|2*k>n, 0, (-1)^(n\2-k)*n!/(n\2-k)!/(n%2+2*k)!/2^(n\2-k)) /* Michael Somos Jun 04 2005 */
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CROSSREFS
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Cf. A000085.
Sequence in context: A055885 A181425 A174505 * A107726 A114159 A033789
Adjacent sequences: A096710 A096711 A096712 * A096714 A096715 A096716
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KEYWORD
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sign,tabl
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AUTHOR
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Eric W. Weisstein, Jul 04, 2004
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STATUS
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approved
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