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