editing
proposed
G. C. Greubel, <a href="/A143229/b143229_1.txt">Table of n, a(n) for n = 0..1000</a>
A143229[n_]:= PartitionsP[n]*Sum[PartitionsP[k], {k, 0, n}];
Table[A143229[n], {n, 0, 50}] (* G. C. Greubel, Aug 27 2024 *)
(Magma)
A143229:= func< n | NumberOfPartitions(n)*(&+[NumberOfPartitions(k): k in [0..n]]) >;
[A143229(n): n in [0..50]]; // G. C. Greubel, Aug 27 2024
(SageMath)
def p(n): return number_of_partitions(n) # A000041
def A143229(n): return p(n)*sum(p(k) for k in range(n+1))
[A143229(n) for n in range(51)] # G. C. Greubel, Aug 27 2024
Cf. A143228, A000041, A000070, A143228.
nonn,changed
nonn
approved
1, 1, 1, 2, 2, 4, 3, 3, 6, 9, 5, 5, 10, 15, 25, 7, 7, 14, 142121, 35, 49, 11, 11, 22, 33, 55, 77, 121, 15, 15, 30, 45, 75, 105, 165, 225, 22, 22, 44, 66, 110, 154, 242, 330, 484, 30, 30, 60, 90, 150, 210, 330, 450, 660, 900, 42, 42, 84, 126, 210, 294, 462, 462630630, 924, 1260, 1764
G. C. Greubel, <a href="/A143228/b143228_1.txt">Rows n = 0..50 of the triangle, flattened</a>
Cf. A000012, A000041, A143229. (row sums).
G. C. Greubel: Added two commas that were missing to separate data values.
G. C. Greubel, <a href="/A143214/b143214_1.txt">Rows n = 1..50 of the triangle, flattened</a>
Edited by G. C. Greubel, Aug 27 2024
