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A003703
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E.g.f. cos(log(1+x)).
(Formerly M2856)
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5
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1, 0, -1, 3, -10, 40, -190, 1050, -6620, 46800, -365300, 3103100, -28269800, 271627200, -2691559000, 26495469000, -238131478000, 1394099824000, 15194495654000, -936096296850000, 29697351895900000
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OFFSET
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0,4
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe and Vaclav Kotesovec, Table of n, a(n) for n = 0..400 (first 100 terms from T. D. Noe)
Vaclav Kotesovec, Graph a(n+1)/a(n)
Vladimir Victorovich Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565
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FORMULA
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a(n) = sum{k=0..n-1, (-1)^(k+1)*T(n-k, k)*sin(pi*(n-k-1)/2)}+0^n; T(n, k)=abs(A008276(n, k)). - Paul Barry, Apr 18 2005
abs(a(n)) = abs(f(n)) with f(n)=prod(i+k,k=1..n) (where i^2=-1). - Yalcin Aktar, Jul 13 2009
a(n) = Sum_{k=0..floor(n/2)} stirling1(n,2*k)*(-1)^(k). - Vladimir Kruchinin, Jan 29 2011
a(n+2)= -a(n+1)*(2*n+1) - a(n)*(1+n^2), a(0)=1, a(1)=0. - Sergei N. Gladkovskii, Aug 17 2012
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EXAMPLE
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1 - x^2 + 3*x^3 - 10*x^4 + 40*x^5 - 190*x^6 + 1050*x^7 - 6620*x^8 + ...
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MAPLE
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a:= n-> add (combinat[stirling1](n, 2*k) * (-1)^(k), k=0..floor(n/2)):
seq (a(n), n=0..20);
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MATHEMATICA
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CoefficientList[Series[Cos[Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 16 2015 *)
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PROG
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(PARI) {a(n) = if( n<0, 0, n! * polcoeff( cos( log( 1 + x + x * O(x^n))), n))} /* Michael Somos, Jul 26 2012 */
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CROSSREFS
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Cf. A009024, A009454.
Sequence in context: A258973 A217885 A216367 * A242651 A231531 A136128
Adjacent sequences: A003700 A003701 A003702 * A003704 A003705 A003706
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KEYWORD
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easy,sign
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AUTHOR
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R. H. Hardin, Simon Plouffe
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STATUS
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approved
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