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%I #6 Jul 30 2018 00:22:18
%S 2,17,66,218,564,1407,3074,6536,12960,24991,46028,83166,145182,249151,
%T 417432,688742,1114978,1782228,2804886,4365560,6709074,10208894,
%U 15368870,22937184,33916388,49763175,72429396,104685554,150234266,214249998,303606838,427780502
%N a(n) = (Sum_{k=1..n} k^3 * p(k) * p(n-k)) * 2/n where p = A000041.
%C See A067567 for a conjecture about this sequence from _Peter Bala_.
%H G. C. Greubel, <a href="/A281708/b281708.txt">Table of n, a(n) for n = 1..5000</a>
%e G.f. = 2*x + 17*x^2 + 66*x^3 + 218*x^4 + 564*x^5 + 1407*x^6 + 3074*x^7 + ...
%t a[n_]:= (2/n)*Sum[k^3*PartitionsP[k]*PartitionsP[n-k], {k,1,n}]; Table[a[n], {n,1,50}] (* _G. C. Greubel_, Jul 29 2018 *)
%o (PARI) {a(n) = if( n<1, 0, sum(k=1, n, k^3 * numbpart(k) * numbpart(n-k)) * 2 / n)};
%Y Cf. A000041, A067567.
%K nonn
%O 1,1
%A _Michael Somos_, Jan 28 2017
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