A259400 a(n) = Sum_{k=0..n} 2^k*p(k), where p(k) is the partition function A000041.

1, 3, 11, 35, 115, 339, 1043, 2963, 8595, 23955, 66963, 181651, 497043, 1324435, 3536275, 9303443, 24442259, 63370643, 164296083, 421197203, 1078654355, 2739598739, 6942291347, 17469994387, 43894109587, 109593687443, 273070880147, 677066241427, 1675109266835

Offset: 0

Author

Vaclav Kotesovec, Jun 26 2015

Keywords

• nonn

Comments

In general, Sum_{k=0..n} (m^k * p(k)) ~ m/(m-1) * m^n * p(n), for m > 1.

Crossrefs

Cf. A000041, A000079, A259401.

Partial sums of A327550.

Programs

Mathematica

Table[Sum[2^k*PartitionsP[k],{k,0,n}],{n,0,40}]

Formula

a(n) ~ 2^(n-1) * exp(Pi*sqrt(2*n/3)) / (n*sqrt(3)).