

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[#[[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^k1).
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



