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A101024 Table of numerators of coefficients of certain rational polynomials. 2
1, 1, 2, 1, 6, 2, 1, 12, 12, 8, 1, 20, 40, 16, 8, 1, 30, 100, 80, 120, 16, 1, 42, 210, 280, 120, 16, 16, 1, 56, 392, 784, 560, 448, 448, 128, 1, 72, 672, 9408, 2016, 896, 1792, 1536, 128, 1, 90, 1080, 4032, 6048, 4032, 13440, 23040, 1152, 256, 1, 110, 1650, 7920 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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. 4, l=1 case, 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

Table of n, a(n) for n=0..58.

W. Lang: Rational polynomials R(n,x)

FORMULA

a(n, m)= numerator(R(n, x)[x^m]), m=0, ..., n, n>=0, with the rational polynomials R(n, x) of degree n defined by R(n, x):=hypergeom([ -n, -1-n], [1/2], -x/2)) = sum(r(n, m)*x^m, m=0..n), n>=0.

The rational polynomials are R(n, x) = 1 + sum((binomial(n, m)*binomial(n+1, m)/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)*binomial(n+1, m)/binomial(2*m, m), m=1..n, n>=1 and r(n, 0)=1, n>=0, else 0.

EXAMPLE

The rows of the rational table are: [1/1]; [1/1,2/1]; [1/1, 6/1, 2/1];[1/1, 12/1, 12/1, 8/5]; ...

CROSSREFS

The table of denominators is given in A101025.

Sequence in context: A208751 A133200 A103881 * A124730 A114283 A106187

Adjacent sequences:  A101021 A101022 A101023 * A101025 A101026 A101027

KEYWORD

nonn,frac,tabl,easy

AUTHOR

Wolfdieter Lang, Nov 30 2004

STATUS

approved

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Last modified July 13 08:26 EDT 2020. Contains 335685 sequences. (Running on oeis4.)