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 A302092 #29 Sep 08 2022 08:46:21 %S A302092 1,1,4,25,765,1300,61306,682306,1713960,1567246464,67208788225, %T A302092 51487177320,33511259427028,2030336608089664,42761083701194302, %U A302092 7549007599307190895,776831192562116876947,3388911887796350381712,649070202541887765091474,43774861324581222789850945 %N A302092 Product of n-th Bell number and n-th Bell number written backwards. %C A302092 Conjecture: in this sequence only two semiprimes (4,25). %F A302092 a(n) = A000110(n)*A004098(n). %e A302092 a(4) = 765 because Bell(4) = 15 and 15*51 = 765. %e A302092 s(5) = 1300 because Bell(5) = 52 and 52*25 = 1300. %p A302092 b:= proc(n) option remember; `if`(n=0, 1, %p A302092 add(b(n-j)*binomial(n-1, j-1), j=1..n)) %p A302092 end: %p A302092 a:= n-> b(n)*(s-> parse(cat(seq(s[-i], i=1..length(s)))))(""||(b(n))): %p A302092 seq(a(n), n=0..25); # _Alois P. Heinz_, Apr 26 2018 %t A302092 BellB[#] FromDigits[Reverse[IntegerDigits[BellB[#]]]]&/@Range[0, 50] %t A302092 # IntegerReverse[#]&/@BellB[Range[0,20]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Dec 29 2019 *) %o A302092 (Magma) [Bell(n)*Seqint(Reverse(Intseq(Bell(n)))): n in [0..30]]; %o A302092 (Perl) use ntheory ":all"; sub Bell {vecsum(map{stirling($_[0],$_,2)} 0..$_[0])} for (0..30) { my $b=Bell($_); print "$_ ",vecprod($b,scalar(reverse($b))),"\n" } # _Dana Jacobsen_, Mar 04 2019 %Y A302092 Cf. A000110, A004098, A133019, A133022. %K A302092 nonn,base,easy %O A302092 0,3 %A A302092 _Vincenzo Librandi_, Apr 01 2018