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A000175
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Related to zeros of Bessel function.
(Formerly M2000 N0790)
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1
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1, 1, 2, 11, 38, 946, 4580, 202738, 3786092, 261868876, 1992367192, 2381255244240, 21411255538848, 2902625722978656, 451716954504285504, 319933105641374465472, 3761845343198709705600
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Constant term of the Rayleigh polynomials. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 20 2010]
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REFERENCES
| D. H. Lehmer, Zeros of the Bessel function J_{nu}(x), Math. Comp., 1 (1943-1945), 405-407.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| H. Jamke, Table of n, a(n) for n=1..100. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 03 2010]
Index entries for sequences related to Bessel functions or polynomials
N. Kishore, The Rayleigh Polynomial, Proc. Amer. Math. Soc. 15, No. 6 (1964), pp. 911-917. [From Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 20 2010]
M. Delest, J.M. Fedou, Enumeration of skew Ferrers diagrams, preprint LaBRI nA degs 89, Bordeaux, Juin 1989 [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 03 2010]
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PROG
| (PARI) alpha(k, n)=if(k<floor(n/2), 2, if(n%2==1, 2, 1)) e(r, k, n)=floor(n/r)-floor(k/r)-floor((n-k)/r) phi2(n)=if(n<3, return(1), return(sum(k=1, floor(n/2), alpha(k, n)*phi2(k)*phi2(n-k)*prod(r=1, n-1, (v+r)^e(r, k, n))))) for(m=1, 30, print1(polcoeff(phi2(m), 0)", ")) [From Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 20 2010]
(PARI) pi0(n)=prod(k=1, n, k^floor(n/k)) J(v, m)=sum(n=0, m, (-1)^n*(x/2)^(2*n+v)/(n!*(n+v)!))+O(x^(2*m+v)) p=J(1, 101)/(2*J(0, 101)); forstep(n=1, 200, 2, print((n+1)/2" "polcoeff(p, n)*pi0((n+1)/2)*2^(n+1))) [From Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 03 2010]
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CROSSREFS
| Sequence in context: A203534 A166989 A143550 * A187259 A125064 A055329
Adjacent sequences: A000172 A000173 A000174 * A000176 A000177 A000178
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Aug 20 2010
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