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A143229 a(n) = A000041(n) * A000070(n).

%I A143229 #13 Aug 27 2024 09:14:46
%S A143229 1,2,8,21,60,133,330,675,1474,2910,5838,10920,20944,37673,68580,
%T A143229 120384,211365,359964,614845,1022630,1701678,2776752,4517016,7232565,
%U A143229 11557350,18201568,28579152,44373420,68634280,105109125,160436916,242692582,365853180,547346709
%N A143229 a(n) = A000041(n) * A000070(n).
%C A143229 Row sums of triangle A143228.
%H A143229 G. C. Greubel, <a href="/A143229/b143229.txt">Table of n, a(n) for n = 0..1000</a>
%F A143229 a(n) = A000041(n) * A000070(n).
%F A143229 a(n) ~ exp(2*sqrt(2*n/3)*Pi)/(8*sqrt(6)*Pi*n^(3/2)) * (1 + (5*Pi/(12*sqrt(6)) - sqrt(3/2)/Pi)/sqrt(n) + (13*Pi^2/1728 - 19/48)/n). - _Vaclav Kotesovec_, Nov 04 2016
%e A143229 a(4) = 60 = A000041(4) * A000070(4) = 5 * 12.
%e A143229 a(4) = 60 = sum of row 4 terms of row 4 in triangle A143228: (5 + 5 + 10 + 15 + 25).
%t A143229 A143229[n_]:= PartitionsP[n]*Sum[PartitionsP[k], {k, 0, n}];
%t A143229 Table[A143229[n], {n,0,50}] (* _G. C. Greubel_, Aug 27 2024 *)
%o A143229 (Magma)
%o A143229 A143229:= func< n | NumberOfPartitions(n)*(&+[NumberOfPartitions(k): k in [0..n]]) >;
%o A143229 [A143229(n): n in [0..50]]; // _G. C. Greubel_, Aug 27 2024
%o A143229 (SageMath)
%o A143229 def p(n): return number_of_partitions(n) # A000041
%o A143229 def A143229(n): return p(n)*sum(p(k) for k in range(n+1))
%o A143229 [A143229(n) for n in range(51)] # _G. C. Greubel_, Aug 27 2024
%Y A143229 Cf. A000041, A000070, A143228.
%K A143229 nonn
%O A143229 0,2
%A A143229 _Gary W. Adamson_, Jul 31 2008
%E A143229 More terms from _Vaclav Kotesovec_, Nov 04 2016