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%I #18 Mar 23 2024 10:51:53
%S 1,3,18,136,1152,10458,99472,978453,9871686,101590654,1062271704,
%T 11253818628,120535386692,1303045817184,14199323523912,
%U 155805565801803,1720024043803542,19090440094335912,212897898182054224,2384431948345110510,26808516659219953680
%N Expansion of (1/x) * Series_Reversion( x * (1 - 3*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/2)} 3^k * binomial(n+k,k) * binomial(4*n+k+2,n-2*k).
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} 3^(n-3*k) * binomial(n+k,k) * binomial(2*n-2*k,n-3*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-3*x-x^3))/x)
%o (PARI) a(n) = sum(k=0, n\2, 3^k*binomial(n+k, k)*binomial(4*n+k+2, n-2*k))/(n+1);
%o (PARI) a(n) = sum(k=0, n\3, 3^(n-3*k)*binomial(n+k, k)*binomial(2*n-2*k, n-3*k))/(n+1);
%Y Cf. A049140, A120985.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 23 2024
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