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 A003703 E.g.f. cos(log(1+x)). (Formerly M2856) 8
 1, 0, -1, 3, -10, 40, -190, 1050, -6620, 46800, -365300, 3103100, -28269800, 271627200, -2691559000, 26495469000, -238131478000, 1394099824000, 15194495654000, -936096296850000, 29697351895900000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS 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 [math.CO], 2010. FORMULA 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 EXAMPLE 1 - x^2 + 3*x^3 - 10*x^4 + 40*x^5 - 190*x^6 + 1050*x^7 - 6620*x^8 + ... MAPLE a:= n-> add (combinat[stirling1](n, 2*k) * (-1)^(k), k=0..floor(n/2)): seq (a(n), n=0..20); MATHEMATICA CoefficientList[Series[Cos[Log[1 + x]], {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 16 2015 *) Table[(-1)^n Im[Pochhammer[1-I, n-1]], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 13 2016 *) PROG (PARI) {a(n) = if( n<0, 0, n! * polcoeff( cos( log( 1 + x + x * O(x^n))), n))} /* Michael Somos, Jul 26 2012 */ CROSSREFS Cf. A009024, A009454. Sequence in context: A258973 A217885 A216367 * A242651 A231531 A136128 Adjacent sequences:  A003700 A003701 A003702 * A003704 A003705 A003706 KEYWORD easy,sign AUTHOR STATUS approved

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