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A003712
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E.g.f. sin(sin(x)) (odd powers only).
(Formerly M2042)
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1
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1, -2, 12, -128, 1872, -37600, 990784, -32333824, 1272660224, -59527313920, 3252626013184, -204354574172160, 14594815769038848, -1174376539738169344, 105595092426069327872, -10530693390637550272512
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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
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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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..50
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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]
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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]
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CROSSREFS
| Sequence in context: A173219 A035351 A201470 * A143136 A097629 A014235
Adjacent sequences: A003709 A003710 A003711 * A003713 A003714 A003715
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KEYWORD
| sign
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net), Simon Plouffe (simon.plouffe(AT)gmail.com)
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