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.
Total /@ Table[n*PartitionsP[n-k], {n, 30}, {k, 0, n - 1}] // Flatten (* Robert Price, Jun 23 2020 *)
Triangle begins:
1;
2, 2;
6, 3, 3;
12, 8, 4, 4;
25, 15, 10, 5, 5;
42, 30, 18, 12, 6, 6;
77, 49, 35, 21, 14, 7, 7;
120, 88, 56, 40, 24, 16, 8, 8;
198, 135, 99, 63, 45, 27, 18, 9, 9;
300, 220, 150, 110, 70, 50, 30, 20, 10, 10;
A182701 := proc(n,k) n*combinat[numbpart](n-k) ; end proc: seq(seq(A182701(n,k),k=1..n),n=1..13) ; # R. J. Mathar, Nov 28 2010
T[n_, k_] := n PartitionsP[n - k];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 19 2019 *)
Total /@ Table[n*PartitionsP[n-k], {n, 38}, {k, n}] // Flatten (* Robert Price, Jun 23 2020 *)
a000070(n) = sum(k=0, n, numbpart(k)); for(n=1, 100, print1(n*a000070(n - 1), ", ")) \\ Indranil Ghosh, Jun 08 2017
from sympy import npartitions as p def a000070(n): return sum([p(k) for k in range(n + 1)]) def a(n): return n*a000070(n - 1) # Indranil Ghosh, Jun 08 2017
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