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A003722
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E.g.f. sin(sinh(x)) (odd powers only).
(Formerly M4541)
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4
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1, 0, -8, -56, 64, 12672, 309376, 2917888, -163782656, -12716052480, -495644917760, -4004259037184, 1359174582304768, 153146435763437568, 9620207941273255936, 142966118908253962240, -62984506636368191946752
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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a(n) = sum(j=1..n+1, (sum(i=0..2*j-1, (-1)^(i+j-1)*(2*j-1-2*i)^(2*n+1)*binomial(2*j-1,i)))/(2^(2*j-1)*(2*j-1)!)); [Vladimir Kruchinin, Jun 09 2011]
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MATHEMATICA
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With[{nn = 50}, Take[CoefficientList[Series[Sin[Sinh[x]], {x, 0, nn}], x] Range[0, nn - 1]!, {2, -1, 2}]] (* Vincenzo Librandi, Apr 11 2014 *)
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PROG
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(Maxima)
a(n):=sum((sum((-1)^(i+j-1)*(2*j-1-2*i)^(2*n+1)*binomial(2*j-1, i), i, 0, 2*j-1))/(2^(2*j-1)*(2*j-1)!), j, 1, n+1); /* Vladimir Kruchinin, Jun 09 2011 */
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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