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A190863
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E.g.f. exp(x*sqrt(1+x^2)).
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1
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1, 1, 1, 4, 13, 16, 61, 736, 1849, -12032, 15481, 1386496, 737221, -139053056, 8889973, 22783492096, 577232881, -4931048505344, 9090479089, 1391155770032128, 747609240061, -492982133885763584, 14533568173741, 214285634326006595584
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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)=n!*sum(k=1..n, (binomial(k/2,(n-k)/2)*((-1)^(n-k)+1))/k!)/2.
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MATHEMATICA
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With[{nn=30}, CoefficientList[Series[Exp[x Sqrt[1+x^2]], {x, 0, nn}], x]Range[0, nn]!] (* Harvey P. Dale, Mar 23 2013 *)
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PROG
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(Maxima)
a(n):=n!*sum((binomial((k)/2, (n-k)/2)*((-1)^(n-k)+1))/k!, k, 1, n)/2;
(PARI) x='x+O('x^66); /* that many terms */
Vec(serlaplace(exp(x*sqrt(1+x^2)))) /* show terms */ /* Joerg Arndt, May 22 2011 */
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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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