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A009537
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Expansion of sin(x)*cosh(log(1+x)).
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1
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0, 1, 0, 2, -12, 51, -300, 2120, -16968, 152677, -1526760, 16794414, -201532980, 2619928663, -36679001268, 550185019124, -8802960306000, 149650325201865, -2693705853633552, 51180411219037658, -1023608224380753180
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OFFSET
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0,4
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LINKS
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FORMULA
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E.g.f.: sin(x)*(1+x+1/(1+x))/2.
a(2*k) = (-1)^(k+1)*k - (2*k)!*Sum_{j=0..k-1} (-1)^j/(2*(2*j+1)!).
a(2*k+1) = (-1)^k + (2*k+1)!*Sum_{j=0..k-1} (-1)^j/(2*(2*j+1)!).
(End)
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MAPLE
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S:= series(sin(x)*(1+x+1/(1+x))/2, x, 51):
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[Sin[x]*Cosh[Log[1+x]], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Aug 20 2015 *)
CoefficientList[Series[((1 + (1 + x)^2)*Sin[x])/(2*(1 + x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jan 23 2015 *)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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