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 A007682 a(n) = -Sum_{k = 0..n-1} (n+k)!a(k)/(2k)!. (Formerly M5044) 1
 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)
 OFFSET 0,6 REFERENCES 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). LINKS H. W. Gould, A class of binomial sums and a series transform, Utilitas Math., 45 (1994), 71-83. (Annotated scanned copy) MAPLE 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; MATHEMATICA 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 *) CROSSREFS Sequence in context: A282323 A224322 A142321 * A125327 A126485 A159031 Adjacent sequences:  A007679 A007680 A007681 * A007683 A007684 A007685 KEYWORD sign,easy,nice AUTHOR STATUS approved

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Last modified February 17 10:59 EST 2019. Contains 320219 sequences. (Running on oeis4.)