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G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^4.
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%I #9 Aug 22 2023 07:57:12

%S 1,1,4,14,56,241,1080,4998,23704,114588,562552,2797138,14057140,

%T 71288385,364360204,1874960408,9706035408,50510552881,264096980192,

%U 1386676113360,7308650513232,38654087828310,205076534841112,1091144400876394,5820924498941668

%N G.f. satisfies A(x) = 1 + x / (1 - x*A(x))^4.

%F If g.f. satisfies A(x) = 1 + x/(1 - x*A(x))^s, then a(n) = Sum_{k=0..n} binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).

%o (PARI) a(n, s=4) = sum(k=0, n, binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));

%Y Cf. A000108, A365113, A365115.

%Y Cf. A321798, A365111.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 22 2023