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a(n) = Sum_{k=0..floor(n/3)} binomial(4*n+2,n-3*k).
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%I #8 Apr 06 2024 10:04:18

%S 1,6,45,365,3078,26565,232831,2063235,18435021,165780758,1498533273,

%T 13603087800,123920995101,1132284232215,10372554403620,95233251146671,

%U 876081280823430,8073359613286509,74513645742072841,688682977876117698,6373025238727622277

%N a(n) = Sum_{k=0..floor(n/3)} binomial(4*n+2,n-3*k).

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

%o (PARI) a(n) = sum(k=0, n\3, binomial(4*n+2, n-3*k));

%Y Cf. A371777, A371778, A371780.

%Y Cf. A066381.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 05 2024