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G.f. satisfies A(x) = ( 1 + x * A(x) * (1 + A(x)) )^2.
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%I #14 Nov 24 2024 08:26:28

%S 1,4,28,248,2480,26688,301648,3531424,42449088,520858496,6497190528,

%T 82146802944,1050370074624,13559126110720,176469550681344,

%U 2313050095245824,30506619439926272,404558181197010944,5391161355764205568,72156618656648237056,969557980700415827968

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

%F G.f.: B(x)^2 where B(x) is the g.f. of A219534.

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

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

%Y Column k=2 of A378239.

%Y Cf. A006318, A371681.

%Y Cf. A219534.

%K nonn,changed

%O 0,2

%A _Seiichi Manyama_, Apr 03 2024