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%I #11 Jan 24 2024 05:59:08
%S 1,3,12,56,287,1564,8895,52195,313655,1920489,11938271,75143016,
%T 477948051,3067190311,19835032603,129129612163,845603794947,
%U 5566269982581,36810651063798,244448822313138,1629413356387998,10898124891668031,73116947514706451
%N Expansion of (1/x) * Series_Reversion( x / ((1+x)^2 * (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(3*n-k+3,n-3*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^2*(1+x+x^3)))/x)
%o (PARI) a(n, s=3, t=1, u=2) = sum(k=0, n\s, binomial(t*(n+1), k)*binomial((t+u)*(n+1)-k, n-s*k))/(n+1);
%Y Cf. A071879, A369481.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 23 2024
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