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%I #9 Aug 14 2015 23:20:09
%S 1,8,424,48896,6672232,1022309408,176808084544,33055112886272,
%T 6507475475389288,1336577286762538496,284198765977135568224,
%U 62135041920796512325952,13901968841738902540019776
%N 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.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SchmidtsProblem.html">Schmidt's Problem</a>
%H Vaclav Kotesovec, <a href="/A092868/a092868.txt">Recurrence (of order 9)</a>
%F a(n) ~ sqrt(3) * 2^(5*n+6) * 3^(2*n+3) / (17^(5/2) * Pi^3 * n^3). - _Vaclav Kotesovec_, Mar 09 2014
%t 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}]
%Y Cf. A000172, A000658.
%Y Fourth row of array A094424.
%K nonn
%O 0,2
%A _Eric W. Weisstein_, Mar 08 2004
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