%I #10 Mar 27 2024 08:53:27
%S 1,5,35,310,3055,32151,353755,4019825,46808750,555621400,6698027100,
%T 81779512155,1009194553315,12567338972700,157725047958100,
%U 1992990741398625,25333585976926275,323725357496659565,4156196637610760235,53585106340408250725,693491493195479127175
%N G.f. A(x) satisfies A(x) = 1 / (1 - x*A(x) / (1+x))^5.
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-1,n-k) * binomial(6*k+4,k)/(k+1).
%F G.f.: A(x) = B(x)^5 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+4, k)/(k+1));
%Y Cf. A349362, A371537, A371538, A371539, A371541.
%Y Cf. A371494, A371495, A371496.
%Y Cf. A371519.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 26 2024
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