OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..57
FORMULA
a(n) = A306680(n^2,n) = [x^(n^2)] (1-x)^(n-1)/((1-x)^n - x^(n+1)).
a(n) ~ c * 2^(1/2 - n/2 + n^2) / (sqrt(Pi)*exp(1/8)*n), where c = Sum_{m = -infinity..+infinity} 1/(2^m * exp(m*(2*m+1)) = 1.77058122254033174512511... if n is even and c = Sum_{m = -infinity..+infinity} 1/(2^(m + 1/2) * exp((m+1)*(2*m+1))) = 1.81629595919505881855931... if n is odd. - Vaclav Kotesovec, Oct 12 2021
MATHEMATICA
a[n_] := Sum[Binomial[n^2 - k, n*k], {k, 0, n}]; Array[a, 13, 0] (* Amiram Eldar, Oct 12 2021 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(n^2-k, n*k));
(PARI) a(n) = polcoef((1-x)^(n-1)/((1-x)^n-x^(n+1)+x*O(x^n^2)), n^2);
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 11 2021
STATUS
approved