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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: A351935 A337574 A166786 * A216370 A225425 A267890

Adjacent sequences:  A003725 A003726 A003727 * A003729 A003730 A003731

KEYWORD

sign

AUTHOR

R. H. Hardin, Simon Plouffe

EXTENSIONS

Corrected title, Joerg Arndt, Apr 23 2011

STATUS

approved

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Last modified June 27 23:11 EDT 2022. Contains 354903 sequences. (Running on oeis4.)