A370242 - OEIS

%I #10 Feb 13 2024 07:36:43

%S 1,2,12,74,480,3202,21756,149746,1040640,7285538,51307212,363057114,

%T 2579270304,18385404546,131429288828,941857237474,6764184258560,

%U 48671099313730,350799656912652,2532218940625642,18303373070813280,132462237913391362,959699439413581692

%N Coefficient of x^n in the expansion of ( 1/(1-x)^2 * (1+x^2) )^n.

%F a(n) = Sum_{k=0..floor(n/2)} binomial(n,k) * binomial(3*n-2*k-1,n-2*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)^2 / (1+x^2) ). See A369208.

%o (PARI) a(n, s=2, t=1, u=2) = sum(k=0, n\s, binomial(t*n, k)*binomial((u+1)*n-s*k-1, n-s*k));

%Y Cf. A288470, A370245.

%Y Cf. A240688, A369208.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Feb 13 2024