A356267 a(n) = Sum_{k=0..n} binomial(2*n, k) * p(k), where p(k) is the partition function A000041.

1, 3, 17, 97, 583, 3275, 18988, 104821, 584441, 3180889, 17295626, 92225785, 492811733, 2590911097, 13591889993, 70605682273, 365601169939, 1876312271003, 9605682510676, 48809295651049, 247315330613099, 1245888505795725, 6256686417801919, 31260996876796579

Offset

0,2

Links

Table of n, a(n) for n=0..23.

Formula

a(n) ~ erfc(Pi/(2*sqrt(6))) * 2^(2*n - 3) * exp(Pi*sqrt(2*n/3) + Pi^2/24) / (sqrt(3)*n).

Mathematica

Table[Sum[Binomial[2*n, k] * PartitionsP[k], {k, 0, n}], {n, 0, 30}]

Crossrefs

Cf. A000041, A032443, A218481, A286955, A356268.

Sequence in context: A302871 A010913 A142988 * A056660 A155610 A001541

Adjacent sequences: A356264 A356265 A356266 * A356268 A356269 A356270

Keyword

nonn

Author

Vaclav Kotesovec, Aug 01 2022

Status

approved