A356289 a(n) = Sum_{k=0..n} binomial(2*n, n-k) * v(k), where v(k) is the number of overpartitions of n (A015128).

1, 4, 18, 82, 372, 1676, 7500, 33358, 147570, 649722, 2848524, 12441434, 54155774, 235008672, 1016971480, 4389589484, 18902538548, 81222609020, 348308661820, 1490884718484, 6370468593732, 27176620756392, 115760526170340, 492386739902574, 2091554077819948, 8873225318953248

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

a(n) ~ 2^(2*n - 7/6) * exp(3 * Pi^(4/3) * n^(1/3) / 2^(8/3)) / (sqrt(3) * Pi^(2/3) * n^(2/3)).

Mathematica

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

Crossrefs

Cf. A015128, A266497, A356280, A356281, A356282, A356283, A356290.

Sequence in context: A264927 A257059 A194460 * A100192 A052913 A279285

Adjacent sequences: A356286 A356287 A356288 * A356290 A356291 A356292

Keyword

nonn

Author

Vaclav Kotesovec, Aug 02 2022

Status

approved