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A003716
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Expansion of tan(sinh(x)).
(Formerly M3144)
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0
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1, 3, 37, 1015, 47881, 3459819, 354711853, 48961863007, 8754050024209, 1967989239505875, 543326939019354421, 180718022989699819207, 71275877445849484090393, 32890432371345908634652347, 17555593768891213894861569085
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| a(n)=sum(k=1..n, ((-1)^(k-1)+1)/(2^k*k!)*sum(i=0..k, (-1)^i*(k-2*i)^n*binomial(k,i))*(sum(j=1..k, j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k,j)))); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 20 2011]
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MATHEMATICA
| Tan[ Sinh[ x ] ] (* Odd Part *)
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PROG
| (Maxima)
a(n):=sum(((-1)^(k-1)+1)/(2^k*k!)*sum((-1)^i*(k-2*i)^n*binomial(k, i), i, 0, k)*(sum(j!*2^(k-j-1)*(-1)^((k+1)/2+j)*stirling2(k, j), j, 1, k)), k, 1, n); [From Vladimir Kruchinin kru(AT)ie.tusur.ru, Apr 20 2011]
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CROSSREFS
| Sequence in context: A143412 A003717 A201697 * A051396 A113074 A128083
Adjacent sequences: A003713 A003714 A003715 * A003717 A003718 A003719
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KEYWORD
| nonn
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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