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a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n*k,n-k).
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%I #9 Mar 26 2023 10:25:28

%S 1,1,-1,-2,13,-29,-80,1268,-7351,13276,245746,-3632793,27451743,

%T -63909390,-1752952501,34899085656,-370619158447,1779155624299,

%U 23668687715473,-780307293795152,12058261763444876,-107734052276914986,-180664717708949253,30298196609011736398

%N a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n*k,n-k).

%F a(n) = [x^n] 1/(1 - x*(1-x)^n).

%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n*k, n-k));

%Y Cf. A099237, A361835.

%K sign,easy

%O 0,4

%A _Seiichi Manyama_, Mar 26 2023