|
%I #16 Oct 13 2021 10:25:18
%S 1,1,0,-19,-493,-12500,2110381,2291797033,2190576317924,
%T 641690166054149,-51808237792071009216,-1670420776971967146820397,
%U -51706433129693385388017540008,3622699946475084834038607930411332,5598748000229343046813449019221837072281
%N a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(n*(n-k),n*k).
%H Seiichi Manyama, <a href="/A348321/b348321.txt">Table of n, a(n) for n = 0..69</a>
%F a(n) = [x^(n^2)] (1-x)^(n-1)/((1-x)^n + x^(2*n)) for n > 0.
%t a[n_] := Sum[(-1)^k * Binomial[n*(n - k), n*k], {k, 0, n}]; Array[a, 15, 0] (* _Amiram Eldar_, Oct 12 2021 *)
%o (PARI) a(n) = sum(k=0, n, (-1)^k*binomial(n*(n-k), n*k));
%o (PARI) a(n) = if(n==0, 1, polcoef((1-x)^(n-1)/((1-x)^n+x^(2*n)+x*O(x^n^2)), n^2));
%Y Cf. A238696, A348322.
%K sign
%O 0,4
%A _Seiichi Manyama_, Oct 12 2021
|
