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%I #16 May 21 2021 04:15:32
%S 1,0,-1,-2,-2,1,10,29,63,117,191,265,264,-12,-1014,-3654,-9634,-21929,
%T -45424,-87551,-158289,-267616,-415513,-563200,-561430,12625,2202084,
%U 8368243,23532027,57848882,131000395,279675274,569701663,1114392742,2099105261,3805794420
%N a(n) = Sum_{k=0..n} (-1)^k * binomial(n,k^2).
%H Seiichi Manyama, <a href="/A307093/b307093.txt">Table of n, a(n) for n = 0..3000</a>
%t a[n_] := Sum[(-1)^k * Binomial[n, k^2], {k, 0, n}]; Array[a, 36, 0] (* _Amiram Eldar_, May 20 2021 *)
%o (PARI) {a(n) = sum(k=0, sqrtint(n), (-1)^k*binomial(n, k^2))}
%Y Cf. A000196, A003099, A307094.
%K sign
%O 0,4
%A _Seiichi Manyama_, Mar 24 2019