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 A101022 Table of numerators of coefficients of certain rational polynomials. 2
 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 4, 2, 8, 1, 5, 4, 1, 8, 4, 1, 1, 2, 2, 8, 8, 16, 1, 7, 14, 1, 8, 4, 16, 2, 1, 4, 56, 4, 16, 32, 64, 16, 128, 1, 3, 8, 6, 16, 8, 64, 8, 128, 64, 1, 5, 2, 12, 16, 16, 160, 16, 128, 128, 256, 1, 11, 22, 33, 176, 8, 32, 4, 128, 64, 256, 64, 1, 2, 44, 22, 88, 32 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,6 COMMENTS These rational polynomials R(n;x) appear in the evaluation of an integral in thermal field theories in the Bose case. See the Haber and Weldon reference eq. (D1), l. 2, p. 1857 and the W. Lang link. REFERENCES H. E. Haber and H. A. Weldon, On the relativistic Bose-Einstein integrals, J. Math. Phys. 23(10) (1982) 1852-1858. LINKS W. Lang: Rational polynomials R(n,x) FORMULA a(n, m)= numerator(R(n, x)[x^m]), m=0, ..., n-1, n>=1, with the rational polynomials R(n, x) of degree n-1 defined by R(n, x):=hypergeom([1, 1, 1-n], [3/2, 2], -x/2)) = sum(R(n, m)*x^m, m=0..n-1), n>=1. The rational polynomials are R(n, x) = 1 + sum(binomial(n-1, m)/((m+1)*(2*m+1)*binomial(2*m, m))*(2*x)^m, m=1..n-1), n>=1. a(n, m)=numerator(R(n, m)) with R(n, m) = binomial(n-1, m)/((m+1)*(2*m+1)*binomial(2*m, m))*2^m, m=1..n-1, n=1, 2, ... and R(n, 0)=1, n>=1, else 0. EXAMPLE The rows of the rational table are: [1/1]; [1/1, 1/6]; [1/1, 1/3, 2/45]; [1/1, 1/2, 2/15, 1/70]; ... CROSSREFS The table of denominators is given in A101023. Sequence in context: A136610 A326371 A226304 * A241153 A213852 A051064 Adjacent sequences:  A101019 A101020 A101021 * A101023 A101024 A101025 KEYWORD nonn,frac,tabl,easy AUTHOR Wolfdieter Lang, Nov 30 2004 STATUS approved

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