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A191499
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E.g.f. sqrt(1+tan(2*x)).
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1
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1, 1, -1, 11, -47, 601, -5521, 86771, -1296287, 25482481, -527699041, 12800059931, -335639304527, 9794548687561, -308817517422961, 10573293809103491, -388317397661640767, 15275057087004591841, -639584224876056953281, 28426125263460829489451, -1335823888802587475761007
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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_{m=0,..,(n-1)/2} ( binomial(2*n-4*m-2,n-2*m-1)*Sum_{j=0,..,2*m} ( binomial(j+n-2*m-1,n-2*m-1)*(j+n-2*m)!*2^(6*m-n-j+1)*(-1)^(m+n+j+1)*stirling2(n,j+n-2*m)))/(n-2*m) ) ), n>0, a(0)=1.
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MAPLE
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S:= series(sqrt(1+tan(2*x)), x, 31):
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MATHEMATICA
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With[{nn = 50}, CoefficientList[Series[Sqrt[1 + Tan[2*x]], {x, 0, nn}], x]*Range[0, nn]!] (* G. C. Greubel, Feb 28 2017 *)
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PROG
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(Maxima)
a(n):=sum((binomial(2*n-4*m-2, n-2*m-1)*sum(binomial(j+n-2*m-1, n-2*m-1)*(j+n-2*m)!*2^(6*m-n-j+1)*(-1)^(m+n+j+1)*stirling2(n, j+n-2*m), j, 0, 2*m))/(n-2*m), m, 0, (n-1)/2);
(PARI) x='x + O('x^50); Vec(serlaplace(sqrt(1 + tan(2*x)))) \\ G. C. Greubel, Feb 28 2017
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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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