A356269 a(n) = Sum_{k=0..n} binomial(2*k, k) * p(k), where p(k) is the partition function A000041.

1, 3, 15, 75, 425, 2189, 12353, 63833, 346973, 1805573, 9565325, 49069517, 257289529, 1307750129, 6723491129, 34024174649, 172873744739, 865954792079, 4359881882579, 21679061144579, 108108834714719, 534409071271199, 2642716232918639, 12975671796056639, 63765647596939139

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

a(n) ~ binomial(2*n,n) * p(n) * 4/3.

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

Mathematica

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

Crossrefs

Cf. A000041, A006134, A032443, A218481, A286955, A356267, A356270.

Sequence in context: A136778 A300665 A278398 * A000266 A294340 A059838

Adjacent sequences: A356266 A356267 A356268 * A356270 A356271 A356272

Keyword

nonn

Author

Vaclav Kotesovec, Aug 01 2022

Status

approved