OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..311
FORMULA
a(n) = (1/n) * Sum_{k=1..n} 2^k * binomial(n,k) * binomial(n^2,k-1) for n > 0.
a(n) = (1/(n^2+1)) * Sum_{k=0..n} binomial(n^2+1,k) * binomial((n+1)*n-k,n-k).
a(n) ~ 2^(n - 1/2) * exp(n) * n^(n - 5/2) / sqrt(Pi). - Vaclav Kotesovec, Jul 31 2021
MATHEMATICA
a[0] = 1; a[n_] := Sum[2^k * Binomial[n, k] * Binomial[n^2, k - 1], {k, 1, n}] / n; Array[a, 18, 0] (* Amiram Eldar, Jul 25 2020 *)
PROG
(PARI) {a(n) = sum(k=0, n, binomial(n, k) * binomial(n^2+k+1, n)/(n^2+k+1))}
(PARI) {a(n) = if(n==0, 1, sum(k=1, n, 2^k*binomial(n, k) * binomial(n^2, k-1)/n))}
(PARI) {a(n) = sum(k=0, n, binomial(n^2+1, k)*binomial((n+1)*n-k, n-k))/(n^2+1)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 25 2020
STATUS
approved