A364437 - OEIS

%I #6 Jul 25 2023 07:38:05

%S 1,1,6,42,326,2712,23676,214068,1987488,18838464,181548960,1773566208,

%T 17523740592,174814263088,1758342057504,17812729393248,

%U 181581358338528,1861259423846400,19172185074938112,198354225907274496,2060279149742042112

%N G.f. satisfies A(x) = 1 - x*(1 - 2*A(x)^3).

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

%F D-finite with recurrence n*(2*n+1)*a(n) +3*(-11*n^2+14*n-4)*a(n-1) +27*(5*n-7) *(n-2)*a(n-2) -27*(7*n-16)*(n-3)*a(n-3) +81*(n-3)*(n-4)*a(n-4)=0. - _R. J. Mathar_, Jul 25 2023

%p A364437 := proc(n)

%p     (-1)^n*add((-2)^k* binomial(n,k) * binomial(3*k+1,n) / (3*k+1),k=0..n) ;

%p end proc:

%p seq(A364437(n),n=0..70); # _R. J. Mathar_, Jul 25 2023

%o (PARI) a(n) = (-1)^n*sum(k=0, n, (-2)^k*binomial(n, k)*binomial(3*k+1, n)/(3*k+1));

%Y Cf. A068764.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jul 24 2023