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A190009
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E.g.f.: exp(tan(x) + tan(x)^2).
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1
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1, 1, 3, 9, 49, 237, 1739, 11557, 105313, 886201, 9596211, 97408641, 1218112465, 14446293669, 204461028347, 2769624924637, 43702453433281, 664858164527089, 11560367630382051, 194954793455032569, 3700614762669466993, 68462595466239603165, 1407869708935659210155
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OFFSET
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0,3
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..468
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FORMULA
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a(n) = Sum_{m=1..n} (Sum_{k=m..n} ((1+(-1)^(n-k))*Sum_{j=k..n} ( j!* stirling2(n,j)*2^(n-j-1)*(-1)^((n+k)/2+j)* binomial(j-1,k-1)) *binomial(m,k-m))/m!), n>0, a(0)=1.
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MATHEMATICA
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With[{nmax = 50}, CoefficientList[Series[Exp[Tan[x] + Tan[x]^2], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jan 11 2018 *)
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PROG
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(Maxima) a(n):=sum(sum((1+(-1)^(n-k))*sum(j!*stirling2(n, j)*2^(n-j-1)*(-1)^((n+k)/2+j)* binomial(j-1, k-1), j, k, n)*binomial(m, k-m), k, m, n)/m!, m, 1, n);
(PARI) x='x+O('x^30); Vec(serlaplace(exp(tan(x)+tan(x)^2))) \\ G. C. Greubel, Jan 11 2018
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CROSSREFS
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Sequence in context: A001530 A316449 A356270 * A012063 A036751 A260156
Adjacent sequences: A190006 A190007 A190008 * A190010 A190011 A190012
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KEYWORD
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nonn
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AUTHOR
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Vladimir Kruchinin, May 03 2011
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EXTENSIONS
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Terms a(18) onward added by G. C. Greubel, Jan 11 2018
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STATUS
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approved
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