A085360 Partial sums of A026905; the convolution of the natural numbers with the partition function.

1, 4, 10, 21, 39, 68, 112, 178, 274, 412, 606, 877, 1249, 1756, 2439, 3353, 4564, 6160, 8246, 10959, 14464, 18971, 24733, 32070, 41365, 53096, 67837, 86296, 109320, 137948

Offset: 1

Author

Jon Perry, Jun 25 2003

Keywords

• nonn

Examples

			a(4) = A026905(1) + A026905(2) + A026905(3) + A026905(4) = 1 + 3 + 6 + 11 = 21.
		

Links

• Riccardo Aragona, Roberto Civino, and Norberto Gavioli, An ultimately periodic chain in the integral Lie ring of partitions, J. Algebr. Comb. (2024). See p. 11.
• Jon Perry, More Partition Function

Crossrefs

Cf. A026905.

Programs

Mathematica

s1=s2=0;lst={};Do[AppendTo[lst,s2+=s1+=PartitionsP[n]],{n,5!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 16 2009 *)

Formula

a(n) = A086716(n) - A086716(n-1). - Vaclav Kotesovec, Jun 23 2015

a(n) ~ sqrt(3) * exp(Pi*sqrt(2*n/3)) / (2*Pi^2). - Vaclav Kotesovec, Jun 23 2015