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A191688
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E.g.f. 1/(1-sin(x)^3)
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0
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1, 0, 0, 6, 0, -60, 720, 546, -40320, 357960, 1693440, -59830914, 414120960, 6693648780, -171958026240, 666035353626, 40363372707840, -832144532031600, -1304413871800320, 365125143426482166, -5976042240729415680
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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(k=1..n, (((-1)^(n-3*k)+1)*sum(i=0..(3*k)/2, (2*i-3*k)^n*binomial(3*k,i)*(-1)^((n+3*k)/2-i)))/2^(3*k)), n>0, a(0)=1.
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[1/(1-Sin[x]^3), {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Oct 11 2011 *)
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PROG
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(Maxima)
a(n):=sum((((-1)^(n-3*k)+1)*sum((2*i-3*k)^n*binomial(3*k, i)*(-1)^((n+3*k)/2-i), i, 0, (3*k)/2))/2^(3*k), k, 1, n);
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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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