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A259400 a(n) = Sum_{k=0..n} 2^k*p(k), where p(k) is the partition function A000041. 3
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 (list; graph; refs; listen; history; text; internal format)
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, A259401.

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

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Last modified July 11 22:52 EDT 2020. Contains 335652 sequences. (Running on oeis4.)