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.

A079330 Numerators of coefficients of odd powers of 1/q in the solution series for tan(x)/x=1.

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%I A079330 #26 Feb 16 2025 08:32:48
%S A079330 1,2,13,146,781,16328,6316012,38759594,9655714457,50134571594,
%T A079330 25626917879,638499558282328,125381104727404588,435948294065152496,
%U A079330 146414084312394268792,1076603090723736731974978
%N A079330 Numerators of coefficients of odd powers of 1/q in the solution series for tan(x)/x=1.
%C A079330 Series contributed by David W. Cantrell.
%D A079330 Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 34, equation 34:7:4 at page 325.
%H A079330 Vaclav Kotesovec, <a href="/A079330/b079330.txt">Table of n, a(n) for n = 1..250</a>
%H A079330 Vaclav Kotesovec, <a href="/A079330/a079330.pdf">Asymptotic of the coefficients A079330 / A088989</a>.
%H A079330 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TancFunction.html">Tanc Function</a>.
%F A079330 a(n)/A088989(n) ~ c * (Pi/2)^(2*n) / n^(4/3), where c = GAMMA(1/3)/(2^(2/3)*3^(1/6)*Pi^(5/3)) = 0.208532... . - _Vaclav Kotesovec_, Aug 19 2014
%t A079330 Last/@Partition[CoefficientList[InverseSeries[Series[x+Cot[x], {x, 0, 50}], q], 1/q], 2]
%Y A079330 Denominators are in A088989.
%Y A079330 Cf. A224196.
%K A079330 nonn,frac
%O A079330 1,2
%A A079330 _Eric W. Weisstein_, Jan 03 2003