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G.f. satisfies A(x) = 1 + x * A(x)^(5/2) * (1 + A(x)^(1/2))^2.
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%I #10 Apr 03 2024 11:12:26

%S 1,4,48,772,14256,285380,6023552,131991940,2974096544,68475379204,

%T 1603913377040,38099316926340,915619571011024,22222175033464260,

%U 543894269096547296,13409307961403740420,332707806061304185408,8301493488646359256580

%N G.f. satisfies A(x) = 1 + x * A(x)^(5/2) * (1 + A(x)^(1/2))^2.

%F G.f. satisfies A(x) = ( 1 + x * A(x)^(5/2) * (1 + A(x)^(1/2)) )^2.

%F G.f.: B(x)^2 where B(x) is the g.f. of A363006.

%F a(n) = 2 * Sum_{k=0..n} binomial(n,k) * binomial(5*n+k+2,n)/(5*n+k+2).

%o (PARI) a(n, r=2, t=5, u=1) = r*sum(k=0, n, binomial(n, k)*binomial(t*n+u*k+r, n)/(t*n+u*k+r));

%Y Cf. A006319, A032349, A371675. A371676, A371678.

%Y Cf. A363006.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Apr 02 2024