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 A340583 #26 Feb 03 2021 23:33:47
%S A340583 1,0,3,1,0,4,1,3,0,7,2,3,4,0,6,2,6,4,7,0,12,4,6,8,7,6,0,8,4,12,8,14,6,
%T A340583 12,0,15,7,12,16,14,12,12,8,0,13,8,21,16,28,12,24,8,15,0,18,12,24,28,
%U A340583 28,24,24,16,15,13,0,12,14,36,32,49,24,48,16,30,13,18,0,28
%N A340583 Triangle read by rows: T(n,k) = A002865(n-k)*A000203(k), 1 <= k <= n.
%C A340583 T(n,k) is the total number of cubic cells added at n-th stage to the right prisms whose bases are the parts of the symmetric representation of sigma(k) in the polycube described in A221529.
%C A340583 Partial sums of column k gives the column k of A221529.
%e A340583 Triangle begins:
%e A340583 1;
%e A340583 0, 3;
%e A340583 1, 0, 4;
%e A340583 1, 3, 0, 7;
%e A340583 2, 3, 4, 0, 6;
%e A340583 2, 6, 4, 7, 0, 12;
%e A340583 4, 6, 8, 7, 6, 0, 8;
%e A340583 4, 12, 8, 14, 6, 12, 0, 15;
%e A340583 7, 12, 16, 14, 12, 12, 8, 0, 13;
%e A340583 8, 21, 16, 28, 12, 24, 8, 15, 0, 18;
%e A340583 12, 24, 28, 28, 24, 24, 16, 15, 13, 0, 12;
%e A340583 14, 36, 32, 49, 24, 48, 16, 30, 13, 18, 0, 28;
%e A340583 ...
%e A340583 For n = 6 the calculation of every term of row 6 is as follows:
%e A340583 --------------------------
%e A340583 k A000203 T(6,k)
%e A340583 --------------------------
%e A340583 1 1 * 2 = 2
%e A340583 2 3 * 2 = 6
%e A340583 3 4 * 1 = 4
%e A340583 4 7 * 1 = 7
%e A340583 5 6 * 0 = 0
%e A340583 6 12 * 1 = 12
%e A340583 . A002865
%e A340583 --------------------------
%e A340583 The sum of row 6 is 2 + 6 + 4 + 7 + 0 + 12 = 31, equaling A138879(6).
%t A340583 A340583[n_, k_] := (PartitionsP[n - k] - PartitionsP[(n - k) - 1])*
%t A340583 DivisorSigma[1, k];
%t A340583 Table[A340583[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* _Robert P. P. McKone_, Jan 25 2021 *)
%Y A340583 Row sums give A138879.
%Y A340583 Column 1 gives A002865.
%Y A340583 Diagonals 1, 3 and 4 give A000203.
%Y A340583 Diagonal 2 gives A000004.
%Y A340583 Diagonals 5 and 6 give A074400.
%Y A340583 Diagonals 7 and 8 give A239050.
%Y A340583 Diagonal 9 gives A319527.
%Y A340583 Diagonal 10 gives A319528.
%Y A340583 Cf. A221529 (partial column sums).
%Y A340583 Cf. A340426 (mirror).
%Y A340583 Cf. A135010, A221530, A245095, A245099, A339278.
%K A340583 nonn,tabl
%O A340583 1,3
%A A340583 _Omar E. Pol_, Jan 15 2021