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A364826 G.f. satisfies A(x) = 1 - x*A(x)^4 * (1 - 3*A(x)).

%I A364826 #18 Aug 09 2023 16:58:33
%S A364826 1,2,22,338,6038,117570,2420758,51833106,1142472150,25749801986,
%T A364826 590737764118,13748997055826,323842714201622,7704914865207362,
%U A364826 184899022770465558,4470200057557410834,108776308617293352534,2662072268791363675650
%N A364826 G.f. satisfies A(x) = 1 - x*A(x)^4 * (1 - 3*A(x)).
%H A364826 Seiichi Manyama, <a href="/A364826/b364826.txt">Table of n, a(n) for n = 0..704</a>
%F A364826 a(n) = (-1)^n * Sum_{k=0..n} (-3)^k * binomial(n,k) * binomial(4*n+k+1,n) / (4*n+k+1).
%F A364826 a(n) = (1/n) * Sum_{k=0..n-1} 2^(n-k) * binomial(n,k) * binomial(5*n-k,n-1-k) for n > 0.
%F A364826 a(n) = (1/n) * Sum_{k=1..n} 2^k * 3^(n-k) * binomial(n,k) * binomial(4*n,k-1) for n > 0.
%o A364826 (PARI) a(n) = (-1)^n*sum(k=0, n, (-3)^k*binomial(n, k)*binomial(4*n+k+1, n)/(4*n+k+1));
%Y A364826 Cf. A025192, A107841, A235347, A364825, A364827.
%Y A364826 Cf. A243667, A260332.
%K A364826 nonn
%O A364826 0,2
%A A364826 _Seiichi Manyama_, Aug 09 2023