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%I #9 Mar 27 2024 08:53:31
%S 1,6,45,410,4110,43746,485237,5547396,64901670,773296320,9350929395,
%T 114464359296,1415620823147,17661466502796,222017667461685,
%U 2809362871991380,35755481454362355,457410181217186886,5878378983480722222,75856853080508789406
%N G.f. A(x) satisfies A(x) = (1 + x*A(x) / (1+x))^6.
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+6,k)/(k+1).
%F G.f.: A(x) = B(x)^6 where B(x) is the g.f. of A349362.
%o (PARI) a(n) = sum(k=0, n, (-1)^(n-k)*binomial(n-1, n-k)*binomial(6*k+6, k)/(k+1));
%Y Cf. A349362, A371537, A371538, A371539, A371540.
%Y Cf. A371521.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 26 2024
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