A366095 - OEIS

%I #10 Sep 29 2023 10:04:29

%S 1,1,1,2,5,11,25,63,162,415,1085,2896,7795,21127,57785,159253,441351,

%T 1229506,3442150,9678358,27315923,77364683,219815829,626375327,

%U 1789627564,5125729137,14714078483,42327358520,121998755959,352272227623,1018915014521

%N Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x)^2 ).

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(n-k+1,n-3*k).

%o (PARI) a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(n-k+1, n-3*k))/(n+1);

%Y Cf. A366071, A366096, A366097.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Sep 29 2023