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A182705 Row sums of triangle A182701.

%I A182705 #23 Jun 23 2020 19:25:48
%S A182705 1,4,12,28,60,114,210,360,603,970,1529,2340,3536,5222,7620,10944,
%T A182705 15555,21816,30343,41740,56994,77132,103684,138312,183450,241696,
%U A182705 316764,412776,535340,690750,887499,1135072,1446060,1834742,2319555,2921616,3667921,4589260
%N A182705 Row sums of triangle A182701.
%H A182705 Robert Price, <a href="/A182705/b182705.txt">Table of n, a(n) for n = 1..2000</a>
%F A182705 a(n) = n * A000070(n-1).
%F A182705 G.f.: x*f'(x), where f(x) = (x/(1 - x))*Product_{k>=1} 1/(1 - x^k). - _Ilya Gutkovskiy_, Jun 08 2017
%t A182705 Total /@ Table[n*PartitionsP[n-k], {n, 38}, {k, n}] // Flatten (* _Robert Price_, Jun 23 2020 *)
%o A182705 (PARI) a000070(n) = sum(k=0, n, numbpart(k));
%o A182705 for(n=1, 100, print1(n*a000070(n - 1), ", ")) \\ _Indranil Ghosh_, Jun 08 2017
%o A182705 (Python)
%o A182705 from sympy import npartitions as p
%o A182705 def a000070(n): return sum([p(k) for k in range(n + 1)])
%o A182705 def a(n): return n*a000070(n - 1) # _Indranil Ghosh_, Jun 08 2017
%Y A182705 Cf. A182700, A182701, A182702, A182704.
%K A182705 nonn
%O A182705 1,2
%A A182705 _Omar E. Pol_, Nov 28 2010