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A367071
G.f. satisfies A(x) = 1 + 2*x + 2*x^2*A(x)^2.
1
1, 2, 2, 8, 16, 48, 136, 384, 1184, 3520, 10944, 34048, 107008, 340480, 1087104, 3502080, 11333120, 36867072, 120491008, 395276288, 1301700608, 4300414976, 14250496000, 47353233408, 157747462144, 526740717568, 1762653863936, 5910312910848
OFFSET
0,2
FORMULA
G.f.: A(x) = 2*(1+2*x) / (1+sqrt(1-8*x^2*(1+2*x))).
a(n) = Sum_{k=0..floor(n/2)} 2^(n-k) * binomial(k+1,n-2*k) * A000108(k).
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
MAPLE
A367071 := proc(n)
add(2^(n-k) * binomial(k+1, n-2*k) * A000108(k), k=0..floor(n/2)) ;
end proc:
seq(A367071(n), n=0..70) ; # R. J. Mathar, Dec 04 2023
PROG
(PARI) a(n) = sum(k=0, n\2, 2^(n-k)*binomial(k+1, n-2*k)*binomial(2*k, k)/(k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Nov 05 2023
STATUS
approved