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

1, 2, 13, 146, 781, 16328, 6316012, 38759594, 9655714457, 50134571594, 25626917879, 638499558282328, 125381104727404588, 435948294065152496, 146414084312394268792, 1076603090723736731974978

Offset: 1

Author

Eric W. Weisstein, Jan 03 2003

Keywords

• nonn
• frac

Comments

Series contributed by David W. Cantrell.

References

• Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 34, equation 34:7:4 at page 325.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..250
• Vaclav Kotesovec, Asymptotic of the coefficients A079330 / A088989.
• Eric Weisstein's World of Mathematics, Tanc Function.

Crossrefs

Denominators are in A088989.

Cf. A224196.

Programs

Mathematica

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

Formula

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