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Search: id:A096949
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| A096949 |
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Numerators of partial sums of series for 3*Artanh(1/3) = (3/2)*ln(2). |
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+0
3
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| 1, 28, 421, 26528, 2148803, 7878956, 2765513941, 74668877408, 3808112752813, 651187280816108, 2511722368895123, 173308843453994432, 7798897955430811787, 1895132203169713822916, 54958833891921780540589
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OFFSET
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0,2
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COMMENT
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Denominators are given in A096950.
From the series of ln((1+x)/(1-x)) for x=1/3, i.e. for ln(2) = 2*sum(((1/3)^(2*k+1))/(2*k+1),k=0..infty).
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FORMULA
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a(n)=numerator(A(n)) with the rational number A(n):= sum(((1/3)^(2*k))/(2*k+1), k=0..n) in lowest terms.
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EXAMPLE
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n=3: 26528/A096950(3) = 26528/25515 = 1.0397021... approximates
3*Artanh(1/3)= 1.039720771...
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CROSSREFS
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Sequence in context: A121798 A024213 A004415 this_sequence A093974 A121803 A022656
Adjacent sequences: A096946 A096947 A096948 this_sequence A096950 A096951 A096952
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jul 16 2004
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