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 A280520 #16 Apr 29 2018 02:13:21 %S A280520 1,0,1,6,1,72,6,2320,72,245765,2320,151182379,245765 %N A280520 Triangle read by rows: T(n,k) = number of increasing sequences of n positive integers with reciprocals adding up to k (k=1,2,...,A055980(n)). %C A280520 T(n,k) = 0 for all k > A055980(n). %C A280520 For n=3,...,11, we have T(n,2) = T(n-1,1). However, T(12,2) > T(11,1). %C A280520 Conjecture: for n in A115515 (i.e., A055980(n+1)=A055980(n)+1), the sequences being enumerated by T(n,A055980(n)) must start with 1. E.g., there is no 10-tuple (x_1,x_2,...,x_10) with 1 < x_1 < ... < x_10 and 1/x_1 + ... + 1/x_10 = 2 (=A055980(10)). %e A280520 Triangle starts with: %e A280520 n=1: 1 %e A280520 n=2: 0 %e A280520 n=3: 1 %e A280520 n=4: 6, 1 %e A280520 n=5: 72, 6 %e A280520 n=6: 2320, 72 %e A280520 n=7: 245765, 2320 %e A280520 n=8: 151182379, 245765 %e A280520 ... %Y A280520 Cf. A280518 (row sums), A006585 (column k=1), A156869 (nondecreasing sequences), A280519 (ordered sequences). %K A280520 nonn,tabf,more %O A280520 1,4 %A A280520 _Max Alekseyev_, Jan 04 2017