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 A111130 Numerator of (n+2)^(n+2)/(n+1)^(n+1) - (n+1)^(n+1)/n^n. 1
 3, 11, 295, 18839, 2178311, 396789539, 104534716847, 37582455061871, 17677524703000879, 10535586945520548779, 7758255095720238886679, 6916955444929558486935047, 7342438845112941396534404087, 9150463033951198007724075565619, 13229286823498332297225524829163231 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS (n+2)^(n+2)/(n+1)^(n+1) - (n+1)^(n+1)/n^n converges very rapidly to e. These can be prime, as is the case for a(0) = 3, a(1) = 11, a(4) = 18839, a(8) = 37582455061871. These are always odd, just as all but the first denominator of A090205 is even. - Jonathan Vos Post, Oct 19 2005 LINKS G. C. Greubel, Table of n, a(n) for n = 0..210 H. J. Brothers and J. A. Knox, New closed-form approximations to the logarithmic constant e, Math. Intelligencer, 20 (1998), 25-29. EXAMPLE 3, 11/4, 295/108, 18839/6912, 2178311/800000, 396789539/145800000, 104534716847/38423222208, ... MATHEMATICA Join[{3}, Numerator[Table[(n + 2)^(n + 2)/(n + 1)^(n + 1) - (n + 1)^(n + 1)/n^n, {n, 1, 25}]]] (* G. C. Greubel, Apr 09 2018 *) PROG (PARI) a(n) = numerator((n+2)^(n+2)/(n+1)^(n+1) - (n+1)^(n+1)/n^n); \\ Michel Marcus, Jun 27 2015 (MAGMA) [Numerator((n+2)^(n+2)/(n+1)^(n+1) - (n+1)^(n+1)/n^n): n in [0..30]]; // G. C. Greubel, Apr 09 2018 CROSSREFS Denominators are 1, 4, 108, 6912, ... - see A090205. Sequence in context: A112357 A205771 A097423 * A264725 A088579 A006938 Adjacent sequences:  A111127 A111128 A111129 * A111131 A111132 A111133 KEYWORD nonn,frac AUTHOR N. J. A. Sloane, Oct 17 2005 STATUS approved

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Last modified August 7 07:54 EDT 2020. Contains 336274 sequences. (Running on oeis4.)