A184357 - OEIS

%I #11 Jul 30 2023 17:12:46

%S 1,2,15,226,5079,151326,5611906,248995090,12862665297,758353907422,

%T 50255751919386,3698524145800452,299324750430958973,

%U 26424096787968560864,2527130527406877225450,260305991718814269022586,28732428200125730917353569

%N a(n) = Sum_{k=0..n} C(n^2-k^2, n-k)*C(k^2, k).

%H Harvey P. Dale, <a href="/A184357/b184357.txt">Table of n, a(n) for n = 0..337</a>

%e a(0) = 1 = 1*1;

%e a(1) = 2 = 1*1 + 1*1;

%e a(2) = 15 = 6*1 + 3*1 + 1*6;

%e a(3) = 226 = 84*1 + 28*1 + 5*6 + 1*84;

%e a(4) = 5079 = 1820*1 + 455*1 + 66*6 + 7*84 + 1*1820;

%e a(5) = 151326 = 53130*1 + 10626*1 + 1330*6 + 120*84 + 9*1820 + 1*53130; ...

%t Table[Sum[Binomial[n^2-k^2,n-k]Binomial[k^2,k],{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, Jul 30 2023 *)

%o (PARI) {a(n)=if(n<0, 0, sum(k=0, n, binomial(n^2-k^2, n-k)*binomial(k^2, k)))}

%Y Cf. A060539, A014062.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jan 15 2011