A226180 Denominators in Taylor series for integral of tan(x)/x.

1, 9, 75, 2205, 25515, 1715175, 79053975, 9577693125, 184530220875, 35266981624875, 4092826025413125, 66711917764366875, 92454016466921484375, 35047468562280596296875, 7641646200968365570359375, 3798425171964103092990703125, 133435000395771234460221796875

Offset: 1

Author

Jean-François Alcover, May 30 2013

Keywords

• nonn
• frac

Comments

Numerators are the same as those from the expansion of tan(x).

Unlike the "sine integral" function Si(x), it seems that there does not exist a "tan integral" function.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A002430 (Numerators for tan(x)), A036279 (Denominators for tan(x)), A000367, A002445.

Programs

Mathematica

a[n_] := Denominator[(-1)^(n-1)*4^n*(4^n-1)*BernoulliB[2*n]/(2*n)!]*(2*n-1); Table[a[n], {n, 1, 17}]

Formula

A036279(n)*(2n-1).