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A009634
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E.g.f. tan(x*cosh(x)), zeros omitted.
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5
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1, 5, 81, 3429, 238273, 25669093, 3923627345, 807194393477, 215176572950017, 72120516857475141, 29686285367774651089, 14721686852776234894885, 8656857857596485141973441, 5955926696414663185424979749
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = b(2*n+1) where b(n) = Sum_{k=1..n} (binomial(n,k)*(((-1)^(k-1)+1)*(Sum_{i=0..k} (k-2*i)^(n-k)*binomial(k,i))*Sum_{j=1..k} j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k,j))/(2^k)). - Vladimir Kruchinin, Apr 21 2011
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MATHEMATICA
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With[{nn=30}, Take[CoefficientList[Series[Tan[Cosh[x]*x], {x, 0, nn}], x] Range[0, nn-1]!, {2, -1, 2}]] (* Harvey P. Dale, Sep 06 2017 *)
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PROG
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(Maxima)
a(n):=b(2*n+1);
b(n):=sum(binomial(n, k)*(((-1)^(k-1)+1)*(sum((k-2*i)^(n-k)*binomial(k, i), i, 0, k))*sum(j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k, j), j, 1, k))/(2^k), k, 1, n); /* Vladimir Kruchinin, Apr 21 2011 */
(PARI)
a(n)={n=2*n+1; sum(k=1, n, binomial(n, k)*(((-1)^(k-1)+1)*(sum(i=0, k, (k-2*i)^(n-k)*binomial(k, i)))*sum(j=1, k, j!*2^(k-j-1)*(-1)^((k+1)/2+j)* stirling(k, j, 2)))/(2^k)); } /* Kruchinin's formula; Joerg Arndt, Apr 22 2011 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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