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Search: id:A059343
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| A059343 |
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Triangle of nonzero coefficients of Hermite polynomials H_n(x) in increasing powers of x. |
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6
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| 1, 2, -2, 4, -12, 8, 12, -48, 16, 120, -160, 32, -120, 720, -480, 64, -1680, 3360, -1344, 128, 1680, -13440, 13440, -3584, 256, 30240, -80640, 48384, -9216, 512, -30240, 302400, -403200, 161280, -23040, 1024, -665280, 2217600, -1774080, 506880, -56320, 2048, 665280, -7983360, 13305600
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 801.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 50.
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LINKS
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T. D. Noe, Rows n=0..100 of triangle, flattened
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
Eric Weisstein's World of Mathematics, Hermite Polynomial
P. Diaconis and A. Gamburd, Random matrices, magic squares and matching polynomials
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EXAMPLE
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1; 2*x; -2+4*x^2; -12*x+8*x^3; ...
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MAPLE
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with(orthopoly): h:=proc(n) if n mod 2=0 then expand(x^2*H(n, x)) else expand(x*H(n, x)) fi end: seq(seq(coeff(h(n), x^(2*k)), k=1..1+floor(n/2)), n=0..14); # this gives the signed sequence
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CROSSREFS
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Cf. A059344.
If initial zeros are included, same as A060821.
Sequence in context: A064880 A115011 A110476 this_sequence A112473 A134435 A136718
Adjacent sequences: A059340 A059341 A059342 this_sequence A059344 A059345 A059346
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KEYWORD
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sign,easy,nice,tabf
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jan 27 2001
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EXTENSIONS
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Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 05 2004
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