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 A343831 a(n) = denominator of (1/e) * Sum_{a_1>=1, a_2>=1, ... , a_n>=1} a_1 * a_2 * ... * a_n / (a_1 + a_2 + ... + a_n)!. 3
 1, 3, 120, 2520, 51840, 2494800, 6227020800, 653837184000, 27360571392000, 30411275102208000, 51090942171709440000, 1846572624206069760000, 15511210043330985984000000, 1361108681302294020096000000, 8841761993739701954543616000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 REFERENCES O. Furdui, Limits, Series and Fractional Part Integrals. Problems in Mathematical Analysis, Springer, New York, 2013. See Problem 3.114 and 3.118. LINKS Seiichi Manyama, Table of n, a(n) for n = 1..225 Math StackExchange, Compute S_n = Sum_{a_1 a_2 ... a_n >=1} a_1 a_2 ... a_n/(a_1+a_2+...+a_n)! FORMULA b(n) = (1/e) * Sum_{a_1>=1, a_2>=1, ... , a_n>=1} a_1 * a_2 * ... * a_n / (a_1 + a_2 + ... + a_n)! = Sum_{j=0..n} (-1)^(n+j-1) * binomial(n,j) * Sum_{k=0..n+j-1} (-1)^k/k! = Sum_{k=0..n-1} binomial(n-1,k)/(k+n)!. a(n) = denominator of b(n). EXAMPLE 1, 2/3, 31/120, 179/2520, 787/51840, 6631/2494800, 2456299/6227020800, ... MATHEMATICA a[n_] := Denominator @ Sum[Binomial[n - 1, k]/(k + n)!, {k, 0, n - 1}]; Array[a, 20] (* Amiram Eldar, May 01 2021 *) PROG (PARI) a(n) = denominator(sum(j=0, n, (-1)^(n+j-1)*binomial(n, j)*sum(k=0, n+j-1, (-1)^k/k!))); (PARI) a(n) = denominator(sum(k=0, n-1, binomial(n-1, k)/(k+n)!)); CROSSREFS Cf. A343830 (numerator), A343832. Sequence in context: A316127 A317433 A214312 * A185554 A134230 A321109 Adjacent sequences: A343828 A343829 A343830 * A343832 A343833 A343834 KEYWORD nonn,frac AUTHOR Seiichi Manyama, Apr 30 2021 STATUS approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)