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A009210
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Expansion of e.g.f.: exp(sin(x)*cos(x)).
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1
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1, 1, 1, -3, -15, -23, 177, 1253, 1057, -37103, -245471, 371085, 15691665, 76436089, -608056239, -10302629131, -20287425215, 856245051169, 8821231566145, -29959421725155, -1376333505095631, -7591883371988471, 139148719952772849
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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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a(n) = sum(j=0..(n-1)/2, (2^(4*j-n+1)*sum(i=0..(n-2*j)/2,(2*i+2*j-n)^n*binomial(n-2*j,i)*(-1)^(n-j-i))/(n-2*j)!), n>0, a(0)=1. - Vladimir Kruchinin, May 29 2011
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} binomial(n-1,2*k) * (-4)^k * a(n-2*k-1). - Ilya Gutkovskiy, Feb 24 2022
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Exp[Sin[x]*Cos[x]], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Aug 10 2021 *)
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PROG
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(Maxima)
a(n):=sum((2^(4*j-n+1)*sum((2*i+2*j-n)^n*binomial(n-2*j, i)*(-1)^(n-j-i), i, 0, ((n-2*j)/2)))/(n-2*j)!, j, 0, ((n-1)/2)); /* Vladimir Kruchinin, May 29 2011 */
(PARI) x='x+O('x^66); Vec(serlaplace(exp(sin(x)*cos(x)))) /* Joerg Arndt, May 29 2011 */
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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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Definition clarified and prior Mathematica program replaced by Harvey P. Dale, Aug 10 2021
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STATUS
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approved
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