A172170 1 followed by the duplicated entries of A090368.

1, 1, 1, 3, 3, 5, 5, 7, 7, 3, 3, 11, 11, 13, 13, 3, 3, 17, 17, 19, 19, 3, 3, 23, 23, 5, 5, 3, 3, 29, 29, 31, 31, 3, 3, 5, 5, 37, 37, 3, 3, 41, 41, 43, 43, 3, 3, 47, 47, 7, 7, 3, 3, 53, 53, 5, 5, 3, 3, 59, 59, 61, 61, 3, 3, 5, 5, 67, 67, 3, 3, 71, 71, 73, 73, 3, 3, 7, 7, 79, 79, 3, 3, 83, 83, 5, 5

Offset

0,4

Comments

We start from the expansion tan(x)+sec(x) = sum_{n>=1} A099612(n)/A099617(n) * x^n with Taylor coefficients 1, 1, 1/2, 1/3, 5/24, 2/15,...

The first differences of this sequence of fractions are 0, -1/2, -1/6, -1/8, -3/40, -7/144, -31/1008, -113/5760,... which is 0 followed by the negated ratios A034428(n)/(n+1)! = 0, -1/2, -1/6, -3/24, -9/120,....

(The factorial follows because A034428 is obtained by multiplying with 1-x to generate first differences of the o.g.f. and then moving on to the e.g.f.)

The common multiple to reduce numerator and denominator of A034428(n)/A000142(n+1) to the standard coprime representation is this sequence here.

Links

Table of n, a(n) for n=0..86.

Formula

a(2n+1)=a(2n+2) = A090368(n), n>=0.

Crossrefs

Sequence in context: A226482 A338777 A110560 * A233808 A141424 A069902

Adjacent sequences: A172167 A172168 A172169 * A172171 A172172 A172173

Keyword

nonn

Author

Paul Curtz, Jan 28 2010

Status

approved