A369621 - OEIS

%I #9 Jan 28 2024 09:19:26

%S 1,1,2,6,18,57,191,660,2334,8417,30831,114380,428915,1623143,6190876,

%T 23774613,91849846,356735941,1392091107,5455425618,21460947111,

%U 84717452192,335479515201,1332327233554,5305235886691,21176621863427,84720103674498

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

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+1,k) * binomial(2*n-4*k,n-3*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1/(1-x)+x^3))/x)

%o (PARI) a(n) = sum(k=0, n\3, binomial(n+1, k)*binomial(2*n-4*k, n-3*k))/(n+1);

%Y Cf. A369622, A369623.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jan 27 2024