|
%I #40 Mar 29 2024 05:41:44
%S 1,4,22,128,777,4872,31330,205560,1370868,9266104,63343006,437183260,
%T 3042337215,21323543252,150395596016,1066637271424,7602188660799,
%U 54422262148632,391146728466980,2821396586367568,20417766975784066,148200184917042112
%N G.f. A(x) satisfies A(x) = (1 + x*A(x)^(3/4) / (1-x))^4.
%F a(n) = 4 * Sum_{k=0..n} binomial(n-1,n-k) * binomial(3*k+4,k)/(3*k+4).
%F G.f.: A(x) = B(x)^4 where B(x) is the g.f. of A307678.
%F a(n) ~ 9 * 31^(n + 1/2) / (sqrt(Pi) * n^(3/2) * 2^(2*n + 3)). - _Vaclav Kotesovec_, Mar 29 2024
%o (PARI) a(n) = 4*sum(k=0, n, binomial(n-1, n-k)*binomial(3*k+4, k)/(3*k+4));
%Y Cf. A045902, A062109, A371379, A371486, A371517.
%Y Cf. A270386, A307678, A371516.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 27 2024
|
