This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380045 #9 Jan 11 2025 10:26:55
%S A380045 1,1,8,109,2220,60585,2079166,86098929,4179685560,232849349425,
%T A380045 14645304783450,1026614846280441,79371261554884036,
%U A380045 6709919722961129337,615776691767279304822,60968162469515187248545,6478143744223567852425456,735290556968263062361451745,88790542940636437330983140146
%N A380045 E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x)*A(x) )^(1/3).
%F A380045 a(n) = n! * Sum_{k=0..n} 3^k * k^(n-k) * binomial(4*k/3+1/3,k)/( (4*k+1)*(n-k)! ).
%o A380045 (PARI) a(n) = n!*sum(k=0, n, 3^k*k^(n-k)*binomial(4*k/3+1/3, k)/((4*k+1)*(n-k)!));
%Y A380045 Cf. A295238, A380044.
%K A380045 nonn
%O A380045 0,3
%A A380045 _Seiichi Manyama_, Jan 10 2025