A345646 a(n) = Sum_{k=0..n} (4*n)! / (k! * (n-k)!)^4.

1, 48, 45360, 60614400, 114144030000, 249344297250048, 609148118181867264, 1604207350254328934400, 4471935609925802450718000, 13022708340511827298941600000, 39267738740263529465273799855360, 121811974529188978353365962361671680, 386880842128109815466159332537704902400

Offset: 0

Author

Vaclav Kotesovec, Jun 21 2021

Keywords

• nonn

Comments

In general, for fixed m >= 1, Sum_{k=0..n} (m*n)! / (k!*(n-k)!)^m ~ (2*m)^(m*n) / (Pi*n)^(m-1).

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..279

Crossrefs

Column 4 of A306641.

Cf. A306642, A306644.

Programs

Mathematica

Table[Sum[(4*n)! / (k! * (n-k)!)^4, {k, 0, n}], {n, 0, 15}]

Formula

a(n) ~ 2^(12*n) / (Pi*n)^3.