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A191500
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E.g.f. sqrt(1+arctan(2*x))
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0
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1, 1, -1, -5, 17, 249, -1489, -27453, 237537, 6037041, -68649441, -2107439157, 29789919345, 1092524775081, -18492402857265, -781266357571053, 15425010795541185, 739391174869277025, -16695627953904545985, -893468264544135234405, 22725280358984904476625
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listen;
history;
text;
internal format)
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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)=2*n!*sum(k=0..(n-1)/2, ((-1)^(n+k+1)*binomial(2*n-4*k-2,n-2*k-1)*(n-2*k-1)!*(sum(i=0..2*k, (2^(i+4*k-n)*stirling1(i+n-2*k,n-2*k)*binomial(n-1,i+n-2*k-1))/(i+n-2*k)!)))), n>0, a(0)=1.
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[Sqrt[1+ArcTan[2x]], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Dec 20 2021 *)
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PROG
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(Maxima)
a(n):=2*n!*sum(((-1)^(n+k+1)*binomial(2*n-4*k-2, n-2*k-1)*(n-2*k-1)!*(sum((2^(i+4*k-n)*stirling1(i+n-2*k, n-2*k)*binomial(n-1, i+n-2*k-1))/(i+n-2*k)!, i, 0, 2*k))), k, 0, (n-1)/2);
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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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