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 A351642 #10 Jan 28 2023 22:07:58
%S A351642 1,1,2,4,10,26,74,218,668,2116,6928,23254,79998,281694,1011956,
%T A351642 3704900,13815692,52386978,201787950,789178950,3130824160,12589367840,
%U A351642 51287685476,211557376938,883067740514,3728494418330,15916998678040,68672820917088,299331260431104
%N A351642 Number of length n word structures with all distinct runs using an infinite alphabet.
%C A351642 Permuting the symbols will not change the structure.
%C A351642 Equivalently, a(n) is the number of restricted growth strings [s(0), s(1), ..., s(n-1)] where s(0)=0 and s(i) <= 1 + max(prefix) for i >= 1 and all runs are distinct.
%H A351642 Andrew Howroyd, <a href="/A351642/b351642.txt">Table of n, a(n) for n = 0..200</a>
%e A351642 The a(4) = 10 words are 1111, 1112, 1121, 1122, 1211, 1222, 1123, 1223, 1233, 1234.
%o A351642 (PARI) \\ See A351641 for R, S.
%o A351642 seq(n)={my(q=S(n)); concat([1], sum(k=1, n, R(q^k-1)*sum(r=k, n, binomial(r, k)*(-1)^(r-k)/r!) )); }
%Y A351642 Row sums of A351641.
%Y A351642 The initial terms are similar to A206464.
%Y A351642 Cf. A351200, A351638.
%K A351642 nonn
%O A351642 0,3
%A A351642 _Andrew Howroyd_, Feb 15 2022