A225602 a(n) = A002426(n^2), where A002426 is the central trinomial coefficients.

1, 1, 19, 3139, 5196627, 82176836301, 12159131877715993, 16639279789182494873661, 209099036316263774148543463251, 24017537903429183163390175566336055657, 25134265191388162956642519120384003897467908119, 239089990313305548946878880624659134220897530949847409821

Offset: 0

Author

Paul D. Hanna, Aug 03 2013

Keywords

• nonn

Examples

			L.g.f.: L(x) = x + 19*x^2/2 + 3139*x^3/3 + 5196627*x^4/4 + 82176836301*x^5/5 + ...
where exponentiation is an integer series:
exp(L(x)) = 1 + x + 10*x^2 + 1056*x^3 + 1300253*x^4 + 16436676927*x^5 + ... + A225604(n)*x^n + ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..45

Crossrefs

Cf. A225604, A002426.

Programs

Mathematica

Table[Sum[Binomial[n^2, k]*Binomial[n^2 - k, k], {k, 0, Floor[n^2/2]}], {n,0,50}] (* G. C. Greubel, Feb 27 2017 *)

PARI

{a(n)=sum(k=0, n^2\2, binomial(n^2, k)*binomial(n^2-k, k))}
for(n=0, 20, print1(a(n), ", "))

Formula

Logarithmic derivative of A225604 (ignoring the initial term of this sequence).

a(n) = Sum_{k=0..floor(n^2/2)} binomial(n^2, k) * binomial(n^2-k, k).