A378786 - OEIS

%I #10 Dec 07 2024 10:41:39

%S 1,1,6,39,296,2435,21138,190603,1767968,16761424,161697576,1582171216,

%T 15664531716,156637712953,1579664567130,16048129755157,

%U 164085811289360,1687224436103842,17436287104620980,181001686332329224,1886522317836670988,19734386503541838083

%N G.f. A(x) satisfies A(x) = 1 + x * (1+x)^2 * A(x)^4.

%F a(n) = Sum_{k=0..n} binomial(4*k+1,k) * binomial(2*k,n-k)/(4*k+1) = Sum_{k=0..n} binomial(2*k,n-k) * A002293(k).

%o (PARI) a(n, r=1, s=2, t=4, u=0) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));

%Y Cf. A365178, A366216, A366272.

%Y Cf. A002478, A073155, A366221.

%Y Cf. A002293.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Dec 07 2024