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A009442
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E.g.f. log(1+x/cos(x)).
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0
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0, 1, -1, 5, -18, 109, -720, 5977, -56336, 612729, -7453440, 100954061, -1502172672, 24395453861, -429076910080, 8128143367905, -164961704478720, 3571195811862385, -82142328351817728, 2000535014776893973
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listen;
history;
text;
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..19.
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FORMULA
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a(n)=2*n!*sum(m=1..(n-1)/2, ((-1)^(n-1)*sum(j=0..m, binomial((n/2-m+j-1),j)*4^(m-j)*sum(i=0..j, (i-j)^(2*m)*binomial(2*j,i)*(-1)^(m+j-i))))/((n-2*m)*(2*m)!))+(-1)^(n-1)*n!/n. [From Vladimir Kruchinin, Jun 16 2011]
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PROG
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(Maxima)
a(n):=2*n!*sum(((-1)^(n-1)*sum(binomial((n/2-m+j-1), j)*4^(m-j)*sum((i-j)^(2*m)*binomial(2*j, i)*(-1)^(m+j-i), i, 0, j), j, 0, m))/((n-2*m)*(2*m)!), m, 1, (n-1)/2)+(-1)^(n-1)*n!/n; [From Vladimir Kruchinin, Jun 16 2011]
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CROSSREFS
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Sequence in context: A165962 A127756 A158455 * A036688 A009348 A009365
Adjacent sequences: A009439 A009440 A009441 * A009443 A009444 A009445
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KEYWORD
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sign,easy
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AUTHOR
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R. H. Hardin
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EXTENSIONS
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Extended with signs Mar 15 1997 by Olivier Gerard.
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STATUS
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approved
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