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 A003712 E.g.f. sin(sin(x)) (odd powers only). (Formerly M2042) 8
 1, -2, 12, -128, 1872, -37600, 990784, -32333824, 1272660224, -59527313920, 3252626013184, -204354574172160, 14594815769038848, -1174376539738169344, 105595092426069327872, -10530693390637550272512 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS abs(a(n)) has e.g.f. sinh(sinh(x)) (odd powers only). abs(a(n)) is the number of partitions of the set {1, 2, ..., 2*n-1} into an odd number of blocks, each containing an odd number of elements. - Isabel C. Lugo (izzycat(AT)gmail.com), Aug 23 2004 REFERENCES L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 226, 6th line of table. N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe and Vincenzo Librandi, Table of n, a(n) for n = 0..100 (first 50 terms from T. D. Noe) FORMULA a(n) = sum(j=1..n+1, (sum(i=0..(2*j-1)/2, (2*i-2*j+1)^(2*n+1)* binomial(2*j-1,i)*(-1)^(n-i-1))/(4^(j-1)*(2*j-1)!))). [Vladimir Kruchinin, Jun 09 2011] MATHEMATICA With[{max = 50}, Take[CoefficientList[Series[Sin[Sin[x]], {x, 0, max}], x] Range[0, max - 1]!, {2, -1, 2}]] (* Vincenzo Librandi, Apr 11 2014 *) Table[Sum[(-1)^(m + n) (1 + 2k - 2m)^(2n + 1)/(4^k (1 + 2k - m)! m!), {k, 0, n}, {m, 0, k + 1/2}], {n, 0, 20}] (* Vladimir Reshetnikov, Nov 07 2015 *) PROG (Maxima) a(n):=sum((sum((2*i-2*j+1)^(2*n+1)*binomial(2*j-1, i)*(-1)^(n-i-1), i, 0, (2*j-1)/2)/(4^(j-1)*(2*j-1)!)), j, 1, n+1); /* Vladimir Kruchinin, Jun 09 2011 */ CROSSREFS Cf. A359553/A359554. Sequence in context: A253282 A201470 A349268 * A143136 A214224 A214431 Adjacent sequences: A003709 A003710 A003711 * A003713 A003714 A003715 KEYWORD sign AUTHOR STATUS approved

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Last modified February 7 08:55 EST 2023. Contains 360115 sequences. (Running on oeis4.)