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Search: id:A066325
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| A066325 |
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Coefficients of unitary Hermite polynomials He_n(x). |
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+0
5
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| 1, 0, 1, -1, 0, 1, 0, -3, 0, 1, 3, 0, -6, 0, 1, 0, 15, 0, -10, 0, 1, -15, 0, 45, 0, -15, 0, 1, 0, -105, 0, 105, 0, -21, 0, 1, 105, 0, -420, 0, 210, 0, -28, 0, 1, 0, 945, 0, -1260, 0, 378, 0, -36, 0, 1, -945, 0, 4725, 0, -3150, 0, 630, 0, -45, 0, 1, 0, -10395, 0, 17325, 0
(list; table; graph; listen)
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OFFSET
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0,8
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COMMENT
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Also number of involutions on n labeled elements with k fixed points times (-1)^(number of 2-cycles).
Also called normalized Hermite polynomials.
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pg 89,94 (2.3.41,54).
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LINKS
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P. Diaconis and A. Gamburd, Random matrices, magic squares and matching polynomials
E. Elizalde, Cosmology: techniques and observations
D. Foata, Une methode combinatoire pour l'\'{e}tude des fonctions sp\'{e}ciales
Index entries for sequences related to Hermite polynomials
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FORMULA
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T(n, k)=(-2)^((k-n)/2)*n!/(k!*((n-k)/2)!). n-k even. 0 otherwise.
E.g.f. (relative to x): A(x, y)=exp(x*y-x^2/2)
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EXAMPLE
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1; 0,1; -1,0,1; 0,-3,0,1; 3,0,-6,0,1; ...
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CROSSREFS
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Row sums: A001464 (with different signs). Row sums of absolute values: A000085. Cf. A060281.
Sequence in context: A101000 A035653 A126595 this_sequence A099174 A137297 A095710
Adjacent sequences: A066322 A066323 A066324 this_sequence A066326 A066327 A066328
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KEYWORD
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sign,tabl
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Dec 14 2001
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