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Search: id:A158616
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| A158616 |
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Table of expansion coefficients [x^m] of the Rayleigh polynomial of index 2n. |
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+0
2
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| 1, 1, 2, 11, 5, 38, 14, 946, 1026, 362, 42, 4580, 4324, 1316, 132, 202738, 311387, 185430, 53752, 7640, 429, 3786092, 6425694, 4434158, 1596148, 317136, 33134, 1430, 261868876, 579783114, 547167306, 287834558, 92481350, 18631334, 2305702
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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Nand Kishore, The Rayleigh Polynomial, Proc. AMS 15 (6) (1964) 911-917.
Nand Kishore, The Rayleigh Function, Proc. AMS 14 (4) (1963) 527-533.
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EXAMPLE
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The polynomials of low index are Phi(2,x)=Phi(4,x) = 1 ; Phi(6,x)=2 ; Phi(8,x)=11+5x ; Phi(10,x)=38+14x ; Phi(12,x)=946+1026x+362x^2+42x^3 ;
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MAPLE
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sig2n := proc(n, nu) option remember ; if n = 1 then 1/4/(nu+1) ; else add( procname(k, nu)*procname(n-k, nu), k=1..n-1)/(nu+n) ; simplify(%) ; fi; end: Phi2n := proc(n, nu) local k ; 4^n*mul( (nu+k)^(floor(n/k)), k=1..n)*sig2n(n, nu) ; factor(%) ; end: for n from 1 to 14 do rpoly := Phi2n(n, nu) ; print(coeffs(rpoly)) ; od:
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CROSSREFS
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Cf. A000992.
Sequence in context: A009301 A087552 A124688 this_sequence A127821 A114724 A165768
Adjacent sequences: A158613 A158614 A158615 this_sequence A158617 A158618 A158619
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KEYWORD
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nonn,tabf
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AUTHOR
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R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 22 2009
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