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%I #17 Apr 11 2024 10:33:43
%S 1,4,10,21,39,68,112,178,274,412,606,877,1249,1756,2439,3353,4564,
%T 6160,8246,10959,14464,18971,24733,32070,41365,53096,67837,86296,
%U 109320,137948
%N Partial sums of A026905; the convolution of the natural numbers with the partition function.
%H Riccardo Aragona, Roberto Civino, and Norberto Gavioli, <a href="https://doi.org/10.1007/s10801-024-01318-x">An ultimately periodic chain in the integral Lie ring of partitions</a>, J. Algebr. Comb. (2024). See p. 11.
%H Jon Perry, <a href="http://www.users.globalnet.co.uk/~perry/maths/morepartitionfunction/morepartitionfunction.htm">More Partition Function</a>
%F a(n) = A086716(n) - A086716(n-1). - _Vaclav Kotesovec_, Jun 23 2015
%F a(n) ~ sqrt(3) * exp(Pi*sqrt(2*n/3)) / (2*Pi^2). - _Vaclav Kotesovec_, Jun 23 2015
%e a(4) = A026905(1) + A026905(2) + A026905(3) + A026905(4) = 1 + 3 + 6 + 11 = 21.
%t s1=s2=0;lst={};Do[AppendTo[lst,s2+=s1+=PartitionsP[n]],{n,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 16 2009 *)
%Y Cf. A026905.
%K nonn
%O 1,2
%A _Jon Perry_, Jun 25 2003
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