A372020 - OEIS

%I #9 Apr 16 2024 10:26:41

%S 1,4,-4,4,156,-1212,5628,196,-251620,2500484,-12608772,16004,

%T 671151260,-7039845180,37258827516,1585476,-2133978944740,

%U 23052545651460,-125166709730820,174117124,7480512144282780,-82265332158299580,453899597102224380,20390254020

%N G.f. A(x) satisfies A(x) = ( 1 + 16*x*A(x)/(1 - x*A(x)) )^(1/4).

%F a(n) = (1/(n+1)) * Sum_{k=0..n} 16^k * binomial(n/4+1/4,k) * binomial(n-1,n-k).

%o (PARI) a(n) = sum(k=0, n, 16^k*binomial(n/4+1/4, k)*binomial(n-1, n-k))/(n+1);

%Y Cf. A372018, A372019.

%Y Cf. A372005.

%K sign

%O 0,2

%A _Seiichi Manyama_, Apr 15 2024