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A009541
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Expansion of sin(x)*exp(sin(x)).
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1
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0, 1, 2, 2, -4, -24, -42, 104, 888, 1792, -8086, -68608, -115468, 1203840, 8863806, 5570816, -275344656, -1636425728, 2488177106, 86205304832, 369676840940, -2289265803264, -34139482063962, -73881736609792, 1691837365047912
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n)=sum(k=1..n, (1+(-1)^(n-k))*2^(-k)*sum(i=0..k/2, (-1)^((n+k)/2-i)*binomial(k,i)*(2*i-k)^n)/(k-1)!), [Vladimir Kruchinin (kru(AT)ie.tusur.ru), Apr 19 2011]
a(n) = D^n(x*exp(x)) evaluated at x = 0, where D is the operator sqrt(1-x^2)*d/dx. Cf. A009623. - Peter Bala, Dec 06 2011
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MATHEMATICA
| Sin[ x ]*Exp[ Sin[ x ] ]
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PROG
| (Maxima)
a(n):=sum((1+(-1)^(n-k))*2^(-k)*sum((-1)^((n+k)/2-i)*binomial(k, i)*(2*i-k)^n, i, 0, k/2)/(k-1)!, k, 1, n); [Vladimir Kruchinin (kru(AT)ie.tusur.ru), Apr 19 2011]
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CROSSREFS
| A009623.
Sequence in context: A175185 A062267 A128501 * A176161 A006829 A154594
Adjacent sequences: A009538 A009539 A009540 * A009542 A009543 A009544
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KEYWORD
| sign,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Extended with signs Mar 15 1997 by Olivier Gerard.
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