This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A233004 #14 Mar 25 2025 14:51:24 %S A233004 0,1,0,12,60,540,0,20160,181440,907200,19958400,359251200,1556755200, %T A233004 32691859200,0,10461394944000,177843714048000,1600593426432000, %U A233004 60822550204416000,608225502044160000,38318206628782080000,702500454861004800000,12926008369442488320000 %N A233004 Pt(n) mod n!, where Pt(n) is product of first n positive triangular numbers (A000217). %C A233004 Pt(n) = n!*(n+1)! / 2^n. %C A233004 Pt(n) mod n! = 0 if and only if 2^n divides (n+1)!, that is, n+1 is a power of 2. Thus indices of zeros are of the form 2^k-1. %o A233004 (Python) %o A233004 f=t=1 %o A233004 for n in range(1,33): %o A233004 t*=n*(n+1)//2 %o A233004 f*=n %o A233004 print(t%f, end=', ') %Y A233004 Cf. A000142, A000217. %Y A233004 Cf. A006472 (triangular factorial, essentially equal to Pt(n)). %Y A233004 Cf. A067667 (Pt(n)/n! for n's of the form 2^k-1). %Y A233004 Cf. A069902, A007917. %K A233004 nonn %O A233004 1,4 %A A233004 _Alex Ratushnyak_, Dec 03 2013