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A003712 E.g.f. sin(sin(x)) (odd powers only).
(Formerly M2042)
5
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

Sequence in context: A209627 A253282 A201470 * A143136 A214224 A214431

Adjacent sequences:  A003709 A003710 A003711 * A003713 A003714 A003715

KEYWORD

sign

AUTHOR

R. H. Hardin, Simon Plouffe

STATUS

approved

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Last modified October 21 16:33 EDT 2018. Contains 316427 sequences. (Running on oeis4.)