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%I #13 Apr 07 2023 02:33:19
%S 1,3,12,27,-75,-444,4734,11532,-466782,1626750,50347410,-708889296,
%T -2196754992,179878246239,-1795732735128,-24691325878980,
%U 953903679982809,-7684914725016600,-226465559200630566,7742131606464606525,-58889021552013912990
%N a(n) = (-1)^n * Sum_{k=0..n} 9^k * binomial(-1/3,k) * binomial(n*k,n-k).
%H Winston de Greef, <a href="/A361847/b361847.txt">Table of n, a(n) for n = 0..468</a>
%F a(n) = [x^n] 1/(1 - 9*x*(1-x)^n)^(1/3).
%o (PARI) a(n) = (-1)^n*sum(k=0, n, 9^k*binomial(-1/3, k)*binomial(n*k, n-k));
%Y Main diagonal of A361840.
%Y Cf. A361835, A361846.
%K sign
%O 0,2
%A _Seiichi Manyama_, Mar 27 2023