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 A090902 a(n) = floor((product of first n triangular numbers)/(sum of first n factorials)). 2
 1, 1, 2, 5, 17, 64, 268, 1236, 6286, 35031, 212401, 1392489, 9817398, 74078419, 595722994, 5086611025, 45961503660, 438168680119, 4395396953168, 46281082011630, 510378647082537, 5882795810558767, 70740717281280862, 885944239324190839, 11537420341016416104 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Floor(Sum (prod(n))/(Product(Sum (n)). Asymptotic formula? LINKS Harvey P. Dale, Table of n, a(n) for n = 1..505 FORMULA a(n) = floor(A000178(n)^(1/n)). EXAMPLE a(4) = floor(((1)*(1+2)*(1+2+3)*(1+2+3+4))/((1)+(1*2)+(1*2*3)+(1*2*3*4))) = 5. MATHEMATICA Do[Print[Floor[ Product[k*(k+1)/2, {k, 1, n}] / Sum[k!, {k, 1, n}] ]], {n, 1, 20}] (* Ryan Propper, Jun 18 2005 *) Module[{nn=20, trs, facs}, trs=Rest[FoldList[Times, 1, Accumulate[Range[ nn]]]]; facs = Accumulate[Range[nn]!]; Floor/@(trs/facs)] (* Harvey P. Dale, Jul 23 2014 *) PROG (PARI) {a(n) = (prod(j=1, n, binomial(j+1, 2))/sum(k=1, n, k!))\1}; for(n=1, 25, print1(a(n), ", ")) \\ G. C. Greubel, Feb 05 2019 (MAGMA) [Floor((&*[Binomial(j+1, 2): j in [1..n]])/(&+[Factorial(k): k in [1..n]])): n in [1..25]]; // G. C. Greubel, Feb 05 2019 (Sage) [floor(prod(binomial(j+1, 2) for j in (1..n))/sum(factorial(k) for k in (1..n))) for n in (1..25)] # G. C. Greubel, Feb 05 2019 CROSSREFS Cf. A090901. Sequence in context: A003456 A109084 A217596 * A150012 A150013 A123166 Adjacent sequences:  A090899 A090900 A090901 * A090903 A090904 A090905 KEYWORD nonn AUTHOR Amarnath Murthy, Dec 12 2003 EXTENSIONS More terms from Ryan Propper, Jun 18 2005 More terms from Harvey P. Dale, Jul 23 2014 STATUS approved

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Last modified October 21 13:24 EDT 2019. Contains 328299 sequences. (Running on oeis4.)