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A003707
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Expansion of ln(1+tan(x)).
(Formerly M3490)
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4
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0, 1, -1, 4, -14, 80, -496, 3904, -34544, 354560, -4055296, 51733504, -724212224, 11070525440, -183218384896, 3266330312704, -62380415842304, 1270842139934720, -27507260369207296, 630424777638805504
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Kruchinin Vladimir Victorovich, Composition of ordinary generating functions, arXiv:1009.2565
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FORMULA
| a(n)=sum((-1)^(k+1)evenp(n+k), k=1,n, (-1)^((n+k)/2)/k*sum(j=k,n, j!/n!*stirling2(n,j)*2^(n-j)*(-1)^(n+j-k)*binomial(j-1,k-1)), n>0 [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 18 2010]
a(n):=sum(m=0..(n-1)/2, sum(j=0..2*m, binomial(j+n-2*m-1,n-2*m-1)*(j+n-2*m)!*2^(2*m-j)*(-1)^(n-m+j-1)*stirling2(n,j+n-2*m))/(n-2*m));
[From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Jan 21 2012]
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MATHEMATICA
| Log[ 1+Tan[ x ] ]
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PROG
| (Maxima) a(n):=sum((-1)^(k+1)*if evenp(n+k) then (-1)^((n+k)/2)/k*sum(j!/n!*stirling2(n, j)*2^(n-j)*(-1)^(n+j-k)*binomial(j-1, k-1), j, k, n) else 0, k, 1, n); [From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Aug 18 2010]
a(n):=sum(sum(binomial(j+n-2*m-1, n-2*m-1)*(j+n-2*m)!*2^(2*m-j)*(-1)^(n-m+j-1)*stirling2(n, j+n-2*m), j, 0, 2*m)/(n-2*m), m, 0, (n-1)/2);
[From Kruchinin Vladimir (kru(AT)ie.tusur.ru), Jan 21 2012]
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CROSSREFS
| Bisections are A002436 and |A024299|.
Sequence in context: A161132 A186638 A187847 * A063862 A024421 A202139
Adjacent sequences: A003704 A003705 A003706 * A003708 A003709 A003710
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KEYWORD
| sign
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net), Simon Plouffe (simon.plouffe(AT)gmail.com)
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