A356268 a(n) = Sum_{k=0..n} binomial(2*n, k) * q(k), where q(k) is the number of partitions into distinct parts (A000009).

1, 3, 11, 62, 289, 1472, 7581, 38014, 184453, 918512, 4548393, 22077762, 107423503, 516720332, 2483445404, 11959145079, 57022343425, 270173627092, 1282971321633, 6047971597490, 28446033085527, 133714464665108, 625893086713686, 2919093380089383, 13596052503945537

Offset

0,2

Links

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

Formula

a(n) ~ erfc(Pi/(4*sqrt(3))) * 2^(2*n - 3) * exp(Pi*sqrt(n/3) + Pi^2/48) / (3^(1/4) * n^(3/4)).

Mathematica

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

Crossrefs

Cf. A000009, A032443, A266232, A307496, A356267.

Sequence in context: A343774 A296321 A203768 * A069725 A291287 A193499

Adjacent sequences: A356265 A356266 A356267 * A356269 A356270 A356271

Keyword

nonn

Author

Vaclav Kotesovec, Aug 01 2022

Status

approved