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 A003728 E.g.f. log(1+x*cos(x)). (Formerly M4208) 2

%I M4208

%S 0,1,-1,-1,6,-31,120,-337,-784,24705,-288000,2451679,-14032128,

%T -17936543,2173889536,-42895630065,583266662400,-5396647099903,

%U 5119183650816,1239561882325439,-36754121131294720,708575518706816481

%N E.g.f. log(1+x*cos(x)).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A003728/b003728.txt">Table of n, a(n) for n = 0..200</a>

%H Vladimir Kruchinin, D. V. Kruchinin, <a href="http://arxiv.org/abs/1103.2582">Composita and their properties</a>, arXiv:1103.2582

%F a(0)=0 and for n>=1, a(n)n!*sum(k=1..n-1,((sum(i=0,floor((k-1)/2),(k-2*i)^(n-k)*binomial(k,i)))*(-1)^((n-k)/2)*((-1)^(n-k)+1))/(2^k*(n-k)!)/k*(-1)^(k-1))+(-1)^(n-1)*(n-1)!. - _Vladimir Kruchinin_, Apr 23 2011

%t With[{nn=30},CoefficientList[Series[Log[1+Cos[x]x],{x,0,nn}],x] Range[0,nn]!] (* From _Harvey P. Dale_, Nov 11 2011 *)

%o (Maxima)

%o a(n) := n! *sum(((sum((k-2*i)^(n-k)*binomial(k,i),i,0,floor((k-1)/2)))*(-1)^((n-k)/2)*((-1)^(n-k)+1))/(2^k*(n-k)!)/k*(-1)^(k-1),k,1,n-1)+(-1)^(n-1)*(n-1)!; /* _Vladimir Kruchinin_, Apr 23 2011 */

%K sign

%O 0,5

%A _R. H. Hardin_, _Simon Plouffe_

%E Corrected title, _Joerg Arndt_, Apr 23 2011

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Last modified August 13 08:18 EDT 2022. Contains 356079 sequences. (Running on oeis4.)