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A364161
G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)).
3
1, 1, 2, 5, 15, 47, 153, 514, 1769, 6205, 22102, 79733, 290721, 1069688, 3966739, 14810348, 55627778, 210046102, 796864028, 3035912900, 11610468138, 44556451207, 171529074168, 662238211929, 2563524741603, 9947573055828, 38687704042595
OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(2*n-5*k+1,n-3*k)/(2*n-5*k+1).
D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(n+1)*a(n-2) +3*(-2*n+3)*a(n-3) +(-2*n+7)*a(n-5) +(n-8)*a(n-6) +(n-8)*a(n-8)=0. - R. J. Mathar, Aug 29 2023
MAPLE
A364161 := proc(n)
add( binomial(n-2*k-1, k)*binomial(2*n-5*k+1, n-3*k)/(2*n5*k+1), k=0..floor(n/3)) ;
end proc:
seq(A364161(n), n=0..80); # R. J. Mathar, Aug 29 2023
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(2*n-5*k+1, n-3*k)/(2*n-5*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 28 2023
STATUS
approved