A259279 a(n) = Sum_{k=0..n} k^2 * A000041(k).

0, 1, 9, 36, 116, 291, 687, 1422, 2830, 5260, 9460, 16236, 27324, 44393, 70853, 110453, 169589, 255422, 380162, 557052, 807852, 1157124, 1642092, 2305987, 3213187, 4436937, 6083673, 8277963, 11192875, 15032040, 20075640, 26650802, 35200178, 46245905, 60476265

Offset: 0

Author

Vaclav Kotesovec, Jun 23 2015

Keywords

• nonn

Crossrefs

Cf. A000041, A182738, A086716.

Programs

Mathematica

Table[Sum[k^2*PartitionsP[k],{k,0,n}],{n,0,50}]

Formula

a(n) ~ n^(3/2) * exp(Pi*sqrt(2*n/3)) / (Pi*2^(3/2)).