A233005 a(n) = floor(Pt(n)/n!), where Pt(n) is product of first n positive triangular numbers (A000217).

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

Offset

1,3

Links

Harvey P. Dale, Table of n, a(n) for n = 1..505

Formula

a(n) = floor((n+1)!/2^n). - Yifan Xie, Mar 05 2023

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[#[[1]]/#[[2]]]&/@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: A360887 A070766 A111772 * A018190 A323930 A187982

Adjacent sequences: A233002 A233003 A233004 * A233006 A233007 A233008

Keyword

nonn

Author

Alex Ratushnyak, Dec 03 2013

Status

approved