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 A335111 a(n) = n! * Sum_{k=0..n-1} (-2)^k / k!. 0
 0, 1, -2, 6, -8, 40, 48, 784, 5248, 49536, 490240, 5403904, 64822272, 842742784, 11798284288, 176974510080, 2831591636992, 48137058942976, 866467058614272, 16462874118651904, 329257482362552320, 6914407129635618816, 152116956851937476608, 3498690007594658430976 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Inverse binomial transform of A000240. LINKS FORMULA G.f.: Sum_{k>=1} k! * x^k / (1 + 2*x)^(k + 1). E.g.f.: x*exp(-2*x) / (1 - x). a(n) = A000023(n) - A122803(n). MATHEMATICA Table[n! Sum[(-2)^k/k!, {k, 0, n - 1}], {n, 0, 23}] nmax = 23; CoefficientList[Series[Sum[k! x^k/(1 + 2 x)^(k + 1), {k, 1, nmax}], {x, 0, nmax}], x] nmax = 23; CoefficientList[Series[x Exp[-2 x]/(1 - x), {x, 0, nmax}], x] Range[0, nmax]! PROG (PARI) a(n) = n! * sum(k=0, n-1, (-2)^k / k!); \\ Michel Marcus, May 23 2020 CROSSREFS Cf. A000023, A000240, A066534, A087981, A122803. Sequence in context: A152158 A291782 A327271 * A095239 A192009 A065953 Adjacent sequences:  A335108 A335109 A335110 * A335112 A335113 A335115 KEYWORD sign AUTHOR Ilya Gutkovskiy, May 23 2020 STATUS approved

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Last modified August 12 07:38 EDT 2020. Contains 336438 sequences. (Running on oeis4.)