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%I #18 Sep 19 2023 12:14:39
%S 1,1,1,1,1,1,2,7,22,57,127,253,468,848,1618,3433,8009,19384,46264,
%T 106369,235179,505955,1079790,2332555,5166405,11737860,27086236,
%U 62676956,144074416,327837356,739787486,1663922487,3751649542,8513640107,19464624667
%N G.f. satisfies A(x) = 1 + x*A(x)*(1 + x^5*A(x)^4).
%F a(n) = Sum_{k=0..floor(n/6)} binomial(n-5*k,k) * binomial(n-k+1,n-5*k) / (n-k+1) = Sum_{k=0..floor(n/6)} binomial(n-k,5*k) * binomial(5*k,k) / (4*k+1).
%o (PARI) a(n) = sum(k=0, n\6, binomial(n-5*k, k)*binomial(n-k+1, n-5*k)/(n-k+1));
%Y Cf. A063019, A182454, A349311, A364539, A364522.
%Y Cf. A005708, A364523, A365732, A365733.
%Y Cf. A002294, A365736.
%K nonn
%O 0,7
%A _Seiichi Manyama_, Sep 19 2023
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