A367071 - OEIS

%I #13 Dec 04 2023 05:35:43

%S 1,2,2,8,16,48,136,384,1184,3520,10944,34048,107008,340480,1087104,

%T 3502080,11333120,36867072,120491008,395276288,1301700608,4300414976,

%U 14250496000,47353233408,157747462144,526740717568,1762653863936,5910312910848

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

%F G.f.: A(x) = 2*(1+2*x) / (1+sqrt(1-8*x^2*(1+2*x))).

%F a(n) = Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(k+1,n-2*k) * A000108(k).

%F D-finite with recurrence (n+2)*a(n) +8*(-n+1)*a(n-2) +8*(-2*n+5)*a(n-3)=0. - _R. J. Mathar_, Dec 04 2023

%p A367071 := proc(n)

%p     add(2^(n-k) * binomial(k+1,n-2*k) * A000108(k),k=0..floor(n/2)) ;

%p end proc:

%p seq(A367071(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023

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

%Y Cf. A000108, A253918, A354733.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 05 2023