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 A233005 floor(Pt(n)/n!), where Pt(n) is product of first n positive triangular numbers (A000217). 1
 1, 1, 3, 7, 22, 78, 315, 1417, 7087, 38981, 233887, 1520268, 10641881, 79814109, 638512875, 5427359437, 48846234937, 464039231906, 4640392319062, 48724119350156, 535965312851718, 6163601097794765, 73963213173537187, 924540164669214843, 12019022140699792968 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 LINKS Harvey P. Dale, Table of n, a(n) for n = 1..505 EXAMPLE a(4) = 7, because, the first four triangular numbers being 1, 3, 6, 10, their product is 180, which divided by 4! is 15/2 = 7.5. a(5) = 22, because, the first five triangular numbers being 1, 3, 6, 10, 15, their product is 2700, which divided by 5! is 45/2 = 22.5. MATHEMATICA With[{nn=30}, Floor[#[]/#[]]&/@Thread[{FoldList[Times, Accumulate[ Range[ nn]]], Range[nn]!}]] (* Harvey P. Dale, Apr 02 2017 *) PROG (Python) f=t=1 for n in range(1, 33):   t*=n*(n+1)/2   f*=n   print str(t/f)+', ', CROSSREFS Cf. A000142, A000217. Cf. A006472 (triangular factorial, essentially equal to Pt(n)). Cf. A067667 (Pt(n)/n! for n's of the form 2^k-1). Sequence in context: A075214 A070766 A111772 * A018190 A323930 A187982 Adjacent sequences:  A233002 A233003 A233004 * A233006 A233007 A233008 KEYWORD nonn AUTHOR Alex Ratushnyak, Dec 03 2013 STATUS approved

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Last modified September 21 20:10 EDT 2021. Contains 347598 sequences. (Running on oeis4.)