cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A336062 Denominators of coefficients associated with the second virial coefficient for rigid spheres with imbedded point dipoles.

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%I A336062 #16 Jul 14 2020 06:53:51
%S A336062 3,75,55125,694575,36018675,2678348673,5934977173125,31414073315625,
%T A336062 7287392748056045625,1197275761489443260625,46668548892583246253625,
%U A336062 1437557979280466067633984375,42189201565839765028388671875,12773202666073647259994954296875,16951256433371736928038065776171875
%N A336062 Denominators of coefficients associated with the second virial coefficient for rigid spheres with imbedded point dipoles.
%D A336062 J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids, John Wiley & Sons, Inc., 1964, pages 210-211.
%F A336062 a(n) = denominator(1/(8 * Pi * (2*n)! * (2*n - 1)) * Integral_{w=0..2*Pi} Integral_{v=0..Pi} Integral_{u=0..Pi} (2 * cos(u) * cos(v) - sin(u) * sin(v) * cos(w))^(2 * n) * sin(u) * sin(v)).
%F A336062 a(n) = denominator(4^n * hypergeom([1, -n], [1/2 - n], 1/4)/((2 * n)! (2 * n - 1) (2 * n + 1)^2)).
%F A336062 a(n) = denominator(4^n*(Sum_{j=0..n} binomial(2*j,j))/(binomial(2*n,n)*(2*n)!*(2*n-1)*(2*n+1)^2)).
%F A336062 A336061(n)/A336062(n) ~ exp(2*n) / (12*sqrt(Pi) * n^(2*n + 7/2)). - _Vaclav Kotesovec_, Jul 14 2020
%e A336062 1/3, 1/75, 29/55125, 11/694575, 13/36018675, 17/2678348673, 523/5934977173125, ...
%t A336062 Table[Denominator[4^k Sum[Binomial[2 j, j]/Binomial[2 k, k], {j, 0, k}]/((2 k)! (2 k - 1) (2 k + 1)^2)], {k, 20}]
%t A336062 Table[Denominator[4^k Hypergeometric2F1[1, -k, 1/2 - k, 1/4]/((2 k)! (2 k - 1) (2 k + 1)^2)], {k, 20}]
%o A336062 (PARI) a(n)={denominator(4^n*sum(j=0, n, binomial(2*j,j))/(binomial(2*n,n)*(2*n)!*(2*n-1)*(2*n+1)^2))} \\ _Andrew Howroyd_, Jul 07 2020
%Y A336062 Cf. A006134, A336061 (numerators).
%K A336062 nonn,easy,frac
%O A336062 1,1
%A A336062 _Jan Mangaldan_, Jul 07 2020