A264411 a(n) = binomial(2*n^2, n).

1, 2, 28, 816, 35960, 2118760, 156238908, 13834413152, 1429702652400, 168899639028120, 22451004309013280, 3316276739861976176, 538884034480519066248, 95533608280955635872536, 18348499272339029224271680, 3795302872076181378439692480, 841141456821158064519401490400, 198852623925936212550698141090040, 49949550731916384239220134110005024

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..300

Formula

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

a(n) ~ (2*n)^(n-1/2) * exp(n-1/4) / sqrt(Pi). - Vaclav Kotesovec, Dec 01 2015

Mathematica

Table[Binomial[2*n^2, n], {n, 0, 15}] (* Vaclav Kotesovec, Dec 01 2015 *)

Prog

(PARI) {a(n)=binomial(2*n^2, n)}
for(n=0, 15, print1(a(n), " "))
(PARI) {a(n)=sum(k=0, n, binomial(n^2, k)*binomial(n^2, n-k))}
for(n=0, 15, print1(a(n), " "))

Crossrefs

Sequence in context: A372164 A372165 A090249 * A370378 A009256 A012725

Adjacent sequences: A264408 A264409 A264410 * A264412 A264413 A264414

Keyword

nonn

Author

Paul D. Hanna, Nov 26 2015

Status

approved