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 A165610 #12 Jul 02 2018 10:08:54
%S A165610 0,0,1,5,31,153,778,3890,20693,114733,676347,4207203,27633048,
%T A165610 190864320,1382896511,10479940137,82864510321,682075572641,
%U A165610 5832740001550,51724150291262,474869801907015,4506715684635739,44152005758171637,445958868912515927,4638590331538888532
%N A165610 The number of patterns of non-papaya words.
%C A165610 Papaya words are defined as palindromes or concatenations of two palindromes.
%H A165610 Tanya Khovanova, <a href="http://blog.tanyakhovanova.com/?p=177">Papaya Words and Numbers</a>
%F A165610 a(n) = A000110(n) - A165137(n).
%e A165610 The only three-character non-papaya pattern is abc - words with all distinct letters. Four-character non-papaya patterns are: aabc, abbc, abcc, abca, abcd.
%t A165610 R[k_?EvenQ] := (1/2)*k*(BellB[1 + k/2] + BellB[k/2]);
%t A165610 R[k_?OddQ] := k*BellB[1 + (k - 1)/2];
%t A165610 b[0] = 1; b[n_] := b[n] = R[n] - Sum[EulerPhi[n/d]*b[d], {d, Most[ Divisors[n]]}];
%t A165610 a[n_] := BellB[n] - b[n];
%t A165610 Array[a, 25] (* _Jean-François Alcover_, Jul 02 2018, after _Andrew Howroyd_ *)
%Y A165610 Cf. A165137, A165135, A165136, A165137, A165611.
%K A165610 nonn
%O A165610 1,4
%A A165610 _Tanya Khovanova_, Sep 22 2009
%E A165610 a(7)-a(25) from _Andrew Howroyd_, Mar 29 2016