A304824 Convolution of central binomial coefficients and partition numbers.

1, 3, 10, 33, 113, 397, 1431, 5249, 19514, 73260, 277100, 1054248, 4029859, 15463765, 59531725, 229816430, 889301153, 3448417251, 13396337155, 52126461984, 203124067675, 792559645912, 3096104725974, 12107810534937, 47395948167885, 185697860476576

Offset: 0

Author

Vaclav Kotesovec, May 19 2018

Keywords

• nonn

Crossrefs

Cf. A000041, A000984, A014329, A304823.

Programs

Mathematica

Table[Sum[PartitionsP[n-k]*Binomial[2*k, k], {k, 0, n}], {n, 0, 25}]

Formula

a(n) ~ 4^n / (QPochhammer[1/4] * sqrt(Pi*n)).