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A007682
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a(n) = -Sum_{k = 0..n-1} (n+k)!a(k)/(2k)!.
(Formerly M5044)
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1
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1, -1, 1, 1, -1, -17, -107, -415, 1231, 56671, 924365, 11322001, 97495687, -78466897, -31987213451, -1073614991039, -26754505127713, -558657850929473, -9259584394031075, -70982644052430799, 3334438016903221111, 240585292388924690959, 10679411902033402697861
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,6
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REFERENCES
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H. W. Gould, A class of binomial sums and a series transform, Utilitas Math., 45 (1994), 71-83.
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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MAPLE
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A007682 := proc(n) option remember; if n=0 then RETURN(1) fi; if n>0 then RETURN((-1)*add((n+k)!*'A007682(k)'/(2*k)!, k=0..n-1 )) fi; end;
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MATHEMATICA
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a[n_] := a[n] = -Sum[(n+k)!*a[k]/(2*k)!, {k, 0, n-1}]; a[0] = 1; Table[a[n], {n, 0, 22}] (* Jean-François Alcover, Jan 27 2014 *)
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CROSSREFS
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KEYWORD
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sign,easy,nice
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AUTHOR
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STATUS
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approved
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