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 A060044 #12 Jul 12 2019 03:32:09
%S A060044 1,-1,1,4,-1,-5,1,6,1,3,-4,-1,-2,8,1,1,-13,-2,-5,13,1,10,23,-6,-1,-11,
%T A060044 -25,12,1,12,27,-20,-2,-21,-49,14,3,31,74,-8,1,5,-13,-62,24,-1,-4,23,
%U A060044 85,-29,1,2,-42,-132,18,-2,-8,42,165,-13,3,14,-42,-195,20,-4,-20,43,229,-30
%N A060044 Triangle of generalized sum of divisors function, read by rows.
%C A060044 Lengths of rows are 1 1 2 2 2 3 3 3 3 ... (A003056).
%H A060044 P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s2-19.1.75">Divisors of numbers and their continuations in the theory of partitions</a>, Proc. London Math. Soc., 19 (1919), 75-113; Coll. Papers II, pp. 303-341.
%F A060044 T(n, k) = sum of (-1)^(k+s_1+s_2+...+s_k) * s_1*s_2*...*s_k where s_1, s_2, ..., s_k are such that s_1*m_1 + s_2*m_2 + ... + s_k*m_k = n and the sum is over all such k-partitions of n.
%F A060044 G.f. for k-th diagonal (the k-th row of the sideways triangle shown in the example): Sum_{ m_1 < m_2 < ... < m_k} q^(m_1+m_2+...+m_k)/((1+q^m_1)*(1+q^m_2)*...*(1+q^m_k))^2 = Sum_n T(n, k)*q^n.
%e A060044 Triangle turned on its side begins:
%e A060044 1 -1 4 -5 6 -4 8 -13 13 ...
%e A060044 1 -1 1 3 -2 1 -5 ...
%e A060044 1 -1 1 -2 ...
%e A060044 For example, T(8,3) = 1.
%Y A060044 Diagonals give A002129, A002130, A060045. Cf. A060043, A060177.
%Y A060044 Cf. A003056.
%K A060044 sign,tabf,easy,nice
%O A060044 1,4
%A A060044 _N. J. A. Sloane_, Mar 19 2001
%E A060044 More terms from _Naohiro Nomoto_, Jan 24 2002