A370218 - OEIS

%I #9 Feb 12 2024 08:39:08

%S 1,3,15,93,639,4578,33423,246816,1838367,13788399,104011140,788315124,

%T 5998380543,45794787678,350619595614,2691082393818,20699166876831,

%U 159515321712480,1231354153215123,9519556856284218,73694926944160164,571201080979318470

%N Coefficient of x^n in the expansion of ( (1+x)^3 / (1-x^3)^3 )^n.

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

%F The g.f. exp( Sum_{k>=1} a(k) * x^k/k ) has integer coefficients and equals (1/x) * Series_Reversion( x / (1+x)^3 * (1-x^3)^3 ). See A369403.

%o (PARI) a(n, s=3, t=3, u=3) = sum(k=0, n\s, binomial(t*n+k-1, k)*binomial(u*n, n-s*k));

%Y Cf. A369403.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 12 2024