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G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3)^3 )^2.
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%I #12 Mar 30 2024 01:41:35

%S 1,2,7,54,419,3644,33366,317672,3113559,31200060,318219653,3292546660,

%T 34475311605,364621943538,3889561661610,41799988930926,

%U 452126713579192,4918321519144206,53773399008883695,590578523863692086,6512515698908748358

%N G.f. satisfies A(x) = ( 1 + x / (1 - x*A(x)^3)^3 )^2.

%H Seiichi Manyama, <a href="/A371617/b371617.txt">Table of n, a(n) for n = 0..934</a>

%F a(n) = Sum_{k=0..n} binomial(6*(n-k)+2,k) * binomial(n+2*k-1,n-k)/(3*(n-k)+1).

%o (PARI) a(n, r=2, s=3, t=0, u=6) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

%Y Cf. A371613, A371615.

%Y Cf. A371616.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 29 2024