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 A123900 (n+3)!/(d(n)*d(n+1)*d(n+2)) where d(n) = cancellation factor in reducing Sum_{k=0...n} 1/k! to lowest terms. 7
 6, 12, 60, 180, 2520, 1008, 18144, 18144, 3991680, 5987520, 155675520, 1089728640, 26153487360, 523069747200, 17784371404800, 12312257126400, 935731541606400, 4678657708032, 12772735542927360, 140500090972200960 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641. LINKS J. Sondow and K. Schalm, Which partial sums of the Taylor series for e are convergents to e? (and a link to the primes 2, 5, 13, 37, 463), II, Gems in Experimental Mathematics (T. Amdeberhan, L. A. Medina, and V. H. Moll, eds.), Contemporary Mathematics, vol. 517, Amer. Math. Soc., Providence, RI, 2010. FORMULA (n+3)!/(A093101(n)*A093101(n+1)*A093101(n+2)) where A093101(n) = GCD(n!,1+n+n(n-1)+...+n!) EXAMPLE a(2) = 60 because (2+3)!/(d(2)*d(3)*d(4)) = 5!/(GCD(2,5)*GCD(6,16)*GCD(24,65)) = 120/2 = 60. MATHEMATICA (A[n_] := If[n==0, 1, n*A[n-1]+1]; d[n_] := GCD[A[n], n! ]; Table[(n+3)!/(d[n]*d[n+1]*d[n+2]), {n, 0, 21}]) CROSSREFS Cf. A000522, A061354, A093101, A123899, A123901. Sequence in context: A117762 A178957 A104362 * A103972 A299855 A121735 Adjacent sequences:  A123897 A123898 A123899 * A123901 A123902 A123903 KEYWORD easy,nonn AUTHOR Jonathan Sondow, Oct 18 2006 STATUS approved

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Last modified May 24 06:53 EDT 2019. Contains 323529 sequences. (Running on oeis4.)