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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
OFFSET
1,3
COMMENTS
Floor(Sum (prod(n))/(Product(Sum (n)). Asymptotic formula?
LINKS
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 A052539
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