A079330 - OEIS

%I #17 Aug 20 2014 11:01:25

%S 1,2,13,146,781,16328,6316012,38759594,9655714457,50134571594,

%T 25626917879,638499558282328,125381104727404588,435948294065152496,

%U 146414084312394268792,1076603090723736731974978

%N Numerators of coefficients of odd powers of 1/q in the solution series for Tan[x]/x=1.

%C Series contributed by David W. Cantrell.

%H Vaclav Kotesovec, <a href="/A079330/b079330.txt">Table of n, a(n) for n = 1..250</a>

%H Vaclav Kotesovec, <a href="/A079330/a079330.pdf">Asymptotic of the coefficients A079330 / A088989</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TancFunction.html">Tanc Function</a>

%F A079330(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 Last/@Partition[CoefficientList[InverseSeries[Series[x+Cot[x], {x, 0, 50}], q], 1/q], 2]

%Y Denominators are in A088989.

%Y Cf. A224196.

%K nonn,frac

%O 1,2

%A _Eric W. Weisstein_, Jan 03 2003