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 A003728 E.g.f. log(1+x*cos(x)). (Formerly M4208) 2
 0, 1, -1, -1, 6, -31, 120, -337, -784, 24705, -288000, 2451679, -14032128, -17936543, 2173889536, -42895630065, 583266662400, -5396647099903, 5119183650816, 1239561882325439, -36754121131294720, 708575518706816481 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties, arXiv:1103.2582 FORMULA 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 MATHEMATICA With[{nn=30}, CoefficientList[Series[Log[1+Cos[x]x], {x, 0, nn}], x] Range[0, nn]!] (* From Harvey P. Dale, Nov 11 2011 *) PROG (Maxima) 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 */ CROSSREFS Sequence in context: A143568 A337574 A166786 * A216370 A225425 A267890 Adjacent sequences:  A003725 A003726 A003727 * A003729 A003730 A003731 KEYWORD sign AUTHOR EXTENSIONS Corrected title, Joerg Arndt, Apr 23 2011 STATUS approved

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Last modified November 27 06:19 EST 2020. Contains 338678 sequences. (Running on oeis4.)