%I #13 Jan 13 2024 10:45:41
%S 1,4,26,202,1729,15730,149249,1460300,14627340,149254996,1545959720,
%T 16212144520,171789072036,1836515799464,19783708310984,
%U 214539449634588,2340148164406642,25658221358522584,282627226176802000,3126081536554547488,34706443838025828198
%N Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x+x^3)^2 ).
%H Seiichi Manyama, <a href="/A368976/b368976.txt">Table of n, a(n) for n = 0..932</a>
%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)} (-1)^k * binomial(2*n+k+1,k) * binomial(5*n-2*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)^2)/x)
%o (PARI) a(n, s=3, t=2, u=2) = sum(k=0, n\s, (-1)^k*binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
%Y Cf. A368970, A368974.
%Y Cf. A368968.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 10 2024
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