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 A233003 #11 Mar 25 2025 14:52:00 %S A233003 0,1,0,36,900,8100,0,25401600,514382400,12859560000,6224027040000, %T A233003 56016243360000,9466745127840000,1855482045056640000,0, %U A233003 6679735362203904000000,13513104637738497792000000,156365925093831188736000000,225792395835492236534784000000,22579239583549223653478400000000 %N A233003 (n!)^2 mod Pt(n), where Pt(n) is product of first n positive triangular numbers (A000217). %C A233003 Indices of zeros appear to be 2^k-1. %e A233003 a(4) = 1*4*9*16 mod 1*3*6*10 = 576 mod 90 = 36. %o A233003 (Python) %o A233003 s=t=1 %o A233003 for n in range(1,33): %o A233003 s*=n*n %o A233003 t*=n*(n+1)//2 %o A233003 print(s%t, end=', ') %Y A233003 Cf. A000142, A000217, A000290, A001044(n!^2). %Y A233003 Cf. A006472 (triangular factorial, essentially equal to Pt(n)). %Y A233003 Cf. A006788 (floor(n!^2/Pt)). %K A233003 nonn %O A233003 1,4 %A A233003 _Alex Ratushnyak_, Dec 03 2013