A378555 - OEIS

%I #13 Nov 30 2024 09:50:09

%S 1,1,9,19,305,156,13233,-23988,688113,-2863070,41085704,-246536784,

%T 2696513885,-19410931916,187672944300,-1481383572516,13522625165601,

%U -111877103550195,994511499413664,-8430550720540365,74061353032540020,-636000265949289978

%N a(n) = Sum_{k=0..n} 9^(n-k) * binomial(n+k-1,k) * binomial(k/3,n-k).

%F a(n) = [x^n] 1/(1 - x*(1 + 9*x)^(1/3))^n.

%t a[n_]:=SeriesCoefficient[1/(1 - x*(1 + 9*x)^(1/3))^n,{x,0,n}]; Array[a,22,0] (* _Stefano Spezia_, Nov 30 2024 *)

%o (PARI) a(n) = sum(k=0, n, 9^(n-k)*binomial(n+k-1, k)*binomial(k/3, n-k));

%Y Cf. A213684, A378554.

%Y Cf. A372126.

%K sign

%O 0,3

%A _Seiichi Manyama_, Nov 30 2024