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

0,2

Links

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

Formula

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

Mathematica

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

Crossrefs

Cf. A000041, A000984, A014329, A304823.

Sequence in context: A071722 A058987 A001558 * A111639 A302076 A149029

Adjacent sequences: A304821 A304822 A304823 * A304825 A304826 A304827

Keyword

nonn

Author

Vaclav Kotesovec, May 19 2018

Status

approved