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

0,2

Comments

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

Links

Table of n, a(n) for n=0..28.

Formula

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

Mathematica

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

Crossrefs

Cf. A000041, A000079, A259401.

Partial sums of A327550.

Sequence in context: A034576 A125672 A107683 * A320087 A014335 A147474

Adjacent sequences: A259397 A259398 A259399 * A259401 A259402 A259403

Keyword

nonn

Author

Vaclav Kotesovec, Jun 26 2015

Status

approved