A365286 - OEIS

%I #7 Aug 31 2023 08:16:47

%S 1,1,2,6,48,600,7920,108360,1693440,32114880,715478400,17616614400,

%T 467505561600,13438170345600,421361740800000,14345678194848000,

%U 524464774215782400,20420391682852761600,844038690729589555200,36981569420732192256000

%N E.g.f. satisfies A(x) = 1 + x*A(x)*exp(x^3*A(x)^2).

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

%o (PARI) a(n) = n!*sum(k=0, n\3, (n-3*k)^k*binomial(n-k+1, n-3*k)/((n-k+1)*k!));

%Y Cf. A358065, A365285, A365287.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Aug 31 2023