A184357 a(n) = Sum_{k=0..n} C(n^2-k^2, n-k)*C(k^2, k).

1, 2, 15, 226, 5079, 151326, 5611906, 248995090, 12862665297, 758353907422, 50255751919386, 3698524145800452, 299324750430958973, 26424096787968560864, 2527130527406877225450, 260305991718814269022586, 28732428200125730917353569

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..337

Example

a(0) = 1 = 1*1;
a(1) = 2 = 1*1 + 1*1;
a(2) = 15 = 6*1 + 3*1 + 1*6;
a(3) = 226 = 84*1 + 28*1 + 5*6 + 1*84;
a(4) = 5079 = 1820*1 + 455*1 + 66*6 + 7*84 + 1*1820;
a(5) = 151326 = 53130*1 + 10626*1 + 1330*6 + 120*84 + 9*1820 + 1*53130; ...

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A060539, A014062.

Sequence in context: A218798 A176337 A145168 * A090301 A297087 A247660

Adjacent sequences: A184354 A184355 A184356 * A184358 A184359 A184360

Keyword

nonn

Author

Paul D. Hanna, Jan 15 2011

Status

approved