A371576 - OEIS

%I #19 Nov 23 2024 11:00:51

%S 1,2,9,44,240,1390,8404,52426,334964,2180928,14418123,96525656,

%T 653077411,4458529390,30674865164,212472058410,1480446579602,

%U 10369560147798,72972217926122,515674254743332,3657933383804959,26036659997517572,185905008055923918

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

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

%F G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A364475.

%o (PARI) a(n, r=2, s=1, t=3, 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 Column k=2 of A378323.

%Y Cf. A001629, A052705, A371577, A371578.

%Y Cf. A270386, A364475.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 28 2024