A297151 a(n) = Sum_{i=0..n} Sum_{j=0..n} Sum_{k=0..n} binomial(n,i)*binomial(n,j)*binomial(n,k)*max(i,j,k).

0, 7, 100, 1128, 11552, 112160, 1052544, 9646336, 86877184, 772010496, 6787635200, 59163619328, 512002867200, 4404129513472, 37687664508928, 321065313239040, 2724508666953728, 23040146455789568, 194245982204461056, 1633162428477865984, 13697353473127874560

Offset: 0

Author

Ognjen Dragoljevic, Dec 26 2017

Keywords

• nonn

Comments

The given closed-form formula is provable.

Crossrefs

Analogous nested sum with only two levels: A100511, and with only one level: A001787.

Programs

Mathematica

Table[n*2^(3n-1)+3n*2^(n-2) Binomial[2n,n],{n,0,20}] (* Harvey P. Dale, Nov 24 2018 *)

Formula

a(n) = n*2^(3*n-1) + 3*n*2^(n-2)*binomial(2*n, n).