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A352643
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Expansion of e.g.f. exp(3 * x * cos(x)).
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3
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1, 3, 9, 18, -27, -552, -3051, -3504, 102825, 1043712, 3192129, -41548416, -653192883, -3033406464, 31367500173, 670266381312, 3916411302609, -40460110970880, -1038593550985479, -6810646726410240, 82445831323038261, 2280185182260854784, 15300402721484153733
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OFFSET
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0,2
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LINKS
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FORMULA
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a(0) = 1; a(n) = 3 * Sum_{k=0..floor((n-1)/2)} (-1)^k * (2*k+1) * binomial(n-1,2*k) * a(n-2*k-1).
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MATHEMATICA
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With[{m = 22}, Range[0, m]! * CoefficientList[Series[Exp[3*x*Cos[x]], {x, 0, m}], x]] (* Amiram Eldar, Mar 26 2022 *)
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PROG
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(PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp(3*x*cos(x))))
(PARI) a(n) = if(n==0, 1, 3*sum(k=0, (n-1)\2, (-1)^k*(2*k+1)*binomial(n-1, 2*k)*a(n-2*k-1)));
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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