A371615 - OEIS

%I #10 Mar 30 2024 02:36:10

%S 1,2,5,34,222,1622,12559,100904,835322,7070574,60922335,532566850,

%T 4711614912,42106192680,379544358032,3446755447528,31504896429042,

%U 289619348156494,2675953520657839,24836797229730316,231461661673958896,2165002179076830442

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

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

%o (PARI) a(n, r=2, s=2, 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, A371617.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 29 2024