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A365243
G.f. satisfies A(x) = 1 + x*A(x)/(1 - x^3*A(x)^2).
3
1, 1, 1, 1, 2, 5, 11, 22, 45, 99, 226, 515, 1168, 2670, 6186, 14467, 33985, 80105, 189636, 451060, 1077225, 2580979, 6201602, 14942480, 36098349, 87417956, 212159347, 515937882, 1257048536, 3068146679, 7500995555, 18366760161, 45037590888, 110588510089
OFFSET
0,5
FORMULA
a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(n-k+1,n-3*k)/(n-k+1).
PROG
(PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(n-k+1, n-3*k)/(n-k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Aug 28 2023
STATUS
approved