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Search: id:A059344
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| A059344 |
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Triangle read by rows: row n consists of the nonzero coefficients of the expansion of 2^n x^n in terms of Hermite polynomials with decreasing subscripts. |
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+0
5
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| 1, 1, 1, 2, 1, 6, 1, 12, 12, 1, 20, 60, 1, 30, 180, 120, 1, 42, 420, 840, 1, 56, 840, 3360, 1680, 1, 72, 1512, 10080, 15120, 1, 90, 2520, 25200, 75600, 30240, 1, 110, 3960, 55440, 277200, 332640, 1, 132, 5940, 110880, 831600, 1995840, 665280, 1, 156
(list; graph; listen)
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OFFSET
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0,4
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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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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].
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FORMULA
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E.g.f.: exp(x^2+y*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 21 2003
a(n, k) = n!/(k! (n-2k)!). - Dean Hickerson (dean.hickerson(AT)yahoo.com), Feb 24 2003
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EXAMPLE
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1; 1; 1,2; 1,6; 1,12,12; 1,20,60; ...
x^2 = 1/2^2*(Hermite(2,x)+2*Hermite(0,x)); x^3 = 1/2^3*(Hermite(3,x)+6*Hermite(1,x)); x^4 = 1/2^4*(Hermite(4,x)+12*Hermite(2,x)+12*Hermite(0,x)); x^5 = 1/2^5*(Hermite(5,x)+20*Hermite(3,x)+60*Hermite(1,x)); x^6 = 1/2^6*(Hermite(6,x)+30*Hermite(4,x)+180*Hermite(2,x)+120*Hermite(0,x)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 21 2003
1 = H(0); 2x = H(1); 4x^2 = H(2)+2H(0); 8x^3 = H(3)+6H(1); etc. where H(k)=Hermite(k,x).
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MATHEMATICA
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a[n_, k_] := n!/k!/(n-2k)!; Flatten[Table[a[n, k], {n, 0, 13}, {k, 0, Floor[n/2]}]]
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CROSSREFS
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Cf. A059343, A060821.
Sequence in context: A139625 A053785 A060173 this_sequence A109193 A083720 A055878
Adjacent sequences: A059341 A059342 A059343 this_sequence A059345 A059346 A059347
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KEYWORD
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nonn,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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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 21 2003
Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 05 2004
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