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%I A367071 #13 Dec 04 2023 05:35:43
%S A367071 1,2,2,8,16,48,136,384,1184,3520,10944,34048,107008,340480,1087104,
%T A367071 3502080,11333120,36867072,120491008,395276288,1301700608,4300414976,
%U A367071 14250496000,47353233408,157747462144,526740717568,1762653863936,5910312910848
%N A367071 G.f. satisfies A(x) = 1 + 2*x + 2*x^2*A(x)^2.
%F A367071 G.f.: A(x) = 2*(1+2*x) / (1+sqrt(1-8*x^2*(1+2*x))).
%F A367071 a(n) = Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(k+1,n-2*k) * A000108(k).
%F A367071 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 A367071 := proc(n)
%p A367071     add(2^(n-k) * binomial(k+1,n-2*k) * A000108(k),k=0..floor(n/2)) ;
%p A367071 end proc:
%p A367071 seq(A367071(n),n=0..70) ; # _R. J. Mathar_, Dec 04 2023
%o A367071 (PARI) a(n) = sum(k=0, n\2, 2^(n-k)*binomial(k+1, n-2*k)*binomial(2*k, k)/(k+1));
%Y A367071 Cf. A000108, A253918, A354733.
%K A367071 nonn
%O A367071 0,2
%A A367071 _Seiichi Manyama_, Nov 05 2023

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