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A068217
Denominators of coefficients in 3*log(sqrt(1+x)) power series.
1
2, 4, 2, 8, 10, 4, 14, 16, 6, 20, 22, 8, 26, 28, 10, 32, 34, 12, 38, 40, 14, 44, 46, 16, 50, 52, 18, 56, 58, 20, 62, 64, 22, 68, 70, 24, 74, 76, 26, 80, 82, 28, 86, 88, 30, 92, 94, 32, 98, 100, 34, 104, 106, 36, 110, 112, 38, 116, 118, 40, 122, 124, 42, 128, 130, 44, 134
OFFSET
1,1
COMMENTS
Numerators are b(n)=(-1)^(n+1) if n==0 (mod 3) b(n)=(-1)^(n+1)*3 otherwise.
FORMULA
a(n) = 2*n/3 if n==0 (mod 3), a(n) = 2*n, otherwise.
3*log(sqrt(1+x)) = (3/2)*log(1+x) = -3 * Sum_{k>=1} (-x)^k/(2*k).
a(n) = 2*A051176(n). - Mitch Harris, Jun 29 2005 [corrected by Kevin Ryde, Oct 30 2021]
MATHEMATICA
a[n_] := If[Mod[n, 3] == 0, 2*n/3, 2*n]; Array[a, 100] (* G. C. Greubel, Sep 21 2018 *)
PROG
(PARI) for(n=1, 100, print1(if(Mod(n, 3)==0, 2*n/3, 2*n), ", ")) \\ G. C. Greubel, Sep 21 2018
CROSSREFS
Cf. A051176 (half).
Sequence in context: A328378 A296429 A065286 * A303603 A308044 A319252
KEYWORD
easy,frac,nonn
AUTHOR
Benoit Cloitre, Mar 30 2002
EXTENSIONS
Log expression corrected by Kevin Ryde, Nov 01 2021
STATUS
approved