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A085360
Partial sums of A026905; the convolution of the natural numbers with the partition function.
2
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
1,2
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.
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
EXAMPLE
a(4) = A026905(1) + A026905(2) + A026905(3) + A026905(4) = 1 + 3 + 6 + 11 = 21.
MATHEMATICA
s1=s2=0; lst={}; Do[AppendTo[lst, s2+=s1+=PartitionsP[n]], {n, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Jul 16 2009 *)
CROSSREFS
Cf. A026905.
Sequence in context: A055908 A325951 A023538 * A265050 A376712 A243738
KEYWORD
nonn
AUTHOR
Jon Perry, Jun 25 2003
STATUS
approved