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 A101020 Table of numerators of coefficients of certain rational polynomials. 2
 1, 1, 1, 1, 4, 2, 1, 9, 6, 2, 1, 16, 24, 32, 8, 1, 25, 200, 40, 40, 8, 1, 36, 150, 160, 360, 32, 16, 1, 49, 294, 490, 280, 56, 112, 16, 1, 64, 1568, 6272, 1120, 3584, 1792, 1024, 128, 1, 81, 864, 14112, 18144, 2016, 5376, 6912, 1152, 128, 1, 100, 1350, 5760, 10080, 8064 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 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), 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, n=0, 1, ..., with the rational polynomials R(n, x) of degree n defined by R(n, x):=hypergeom([ -n, -n], [1/2], x/2) = 1 + sum(r(n, m)*x^m, m=1..n), n>=0. The rational polynomials are R(n, x) = 1 + sum(((binomial(n, m)^2)/binomial(2*m, m))*(2*x)^m, m=1..n), n>=0. a(n, m)=numerator(r(n, m)) with the rational triangle r(n, m) = (2^m)*(binomial(n, m)^2)/binomial(2*m, m)), m=1..n, n=1, 2, ... and r(n, 0)=1, n>=0, else 0. EXAMPLE The rows of the rational table are: [1/1]; [1/1,1/1]; [1/1,4/1,2/3]; [1/1, 9/1, 6/1, 2/5]; ... CROSSREFS The denominator table is given in A101021. Sequence in context: A021241 A016691 A177347 * A160905 A208612 A183157 Adjacent sequences:  A101017 A101018 A101019 * A101021 A101022 A101023 KEYWORD nonn,frac,tabl,easy AUTHOR Wolfdieter Lang, Nov 30 2004 STATUS approved

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Last modified December 7 05:14 EST 2019. Contains 329839 sequences. (Running on oeis4.)