A092868 Coefficients c[r,n] in Schmidt's problem Sum[Binomial[n,k]^r Binomial[n+k,k]^r,{k,0,n}] == Sum[Binomial[n,k]Binomial[n+k,k]c[r,k],{k,0,n}] for r=4.

1, 8, 424, 48896, 6672232, 1022309408, 176808084544, 33055112886272, 6507475475389288, 1336577286762538496, 284198765977135568224, 62135041920796512325952, 13901968841738902540019776

Offset: 0

Author

Eric W. Weisstein, Mar 08 2004

Keywords

• nonn

Links

• Eric Weisstein's World of Mathematics, Schmidt's Problem
• Vaclav Kotesovec, Recurrence (of order 9)

Crossrefs

Cf. A000172, A000658.

Fourth row of array A094424.

Programs

Mathematica

c[4, n_] := Sum[Binomial[2j, j]^3Binomial[n, j]Binomial[k+j, k-j]Binomial[j, n-k]Binomial[k, j]Binomial[2j, k-j], {k, 0, n}, {j, 0, n}]

Formula

a(n) ~ sqrt(3) * 2^(5*n+6) * 3^(2*n+3) / (17^(5/2) * Pi^3 * n^3). - Vaclav Kotesovec, Mar 09 2014