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%I #14 Sep 08 2022 08:45:12
%S 1,1,2,5,17,64,268,1236,6286,35031,212401,1392489,9817398,74078419,
%T 595722994,5086611025,45961503660,438168680119,4395396953168,
%U 46281082011630,510378647082537,5882795810558767,70740717281280862,885944239324190839,11537420341016416104
%N a(n) = floor((product of first n triangular numbers)/(sum of first n factorials)).
%C Floor(Sum (prod(n))/(Product(Sum (n)). Asymptotic formula?
%H Harvey P. Dale, <a href="/A090902/b090902.txt">Table of n, a(n) for n = 1..505</a>
%F a(n) = floor(A000178(n)^(1/n)).
%e a(4) = floor(((1)*(1+2)*(1+2+3)*(1+2+3+4))/((1)+(1*2)+(1*2*3)+(1*2*3*4))) = 5.
%t Do[Print[Floor[ Product[k*(k+1)/2, {k, 1, n}] / Sum[k!, {k, 1, n}] ]], {n, 1, 20}] (* _Ryan Propper_, Jun 18 2005 *)
%t 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 *)
%o (PARI) {a(n) = (prod(j=1,n, binomial(j+1,2))/sum(k=1,n, k!))\1};
%o for(n=1,25, print1(a(n), ", ")) \\ _G. C. Greubel_, Feb 05 2019
%o (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
%o (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
%Y Cf. A090901.
%K nonn
%O 1,3
%A _Amarnath Murthy_, Dec 12 2003
%E More terms from _Ryan Propper_, Jun 18 2005
%E More terms from _Harvey P. Dale_, Jul 23 2014
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