A371578 - OEIS

%I #17 Mar 30 2024 02:37:59

%S 1,2,13,102,916,8880,90607,958794,10426089,115798342,1308035135,

%T 14980661482,173553196140,2030265152576,23948922940698,

%U 284543368174220,3402103050539715,40903437537402792,494215527894112099,5997782678374854902,73078635875447981850

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

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

%F G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A365184.

%o (PARI) a(n, r=2, s=1, t=5, 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. A001629, A052705, A371576, A371577.

%Y Cf. A365184, A371580.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 28 2024