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A172170
1 followed by the duplicated entries of A090368.
1
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.
FORMULA
a(2n+1)=a(2n+2) = A090368(n), n>=0.
CROSSREFS
Sequence in context: A226482 A338777 A110560 * A233808 A141424 A069902
KEYWORD
nonn
AUTHOR
Paul Curtz, Jan 28 2010
STATUS
approved