A378732 - OEIS

%I #11 Dec 06 2024 11:10:35

%S 1,4,10,36,155,704,3384,16844,86097,449344,2384170,12822556,69743953,

%T 382982940,2120323014,11822279232,66327376437,374162700460,

%U 2120999728610,12075668658000,69021358842795,395909382981572,2278286453089574,13149207655326372,76096242994616990

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

%F G.f.: A(x) = (1 + x*B(x))^4 where B(x) is the g.f. of A364743.

%F If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = 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).

%o (PARI) a(n, r=4, s=1, t=0, u=4) = 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. A364743, A371612, A378731.

%Y cf. A365118, A365119.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Dec 05 2024