Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Jan 24 2024 05:55:31
%S 1,2,5,15,51,187,718,2844,11530,47612,199576,847013,3632468,15717041,
%T 68527255,300780438,1327939406,5893299392,26275243626,117635107818,
%U 528631769323,2383660351991,10781500113896,48903885040638,222400899237943,1013841791472632
%N Expansion of (1/x) * Series_Reversion( x / ((1+x) * (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-k+2,n-3*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)*(1+x+x^3)))/x)
%o (PARI) a(n, s=3, t=1, u=1) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
%Y Cf. A071879, A369482.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 23 2024