A371045 - OEIS

%I #8 Mar 09 2024 08:16:30

%S 1,0,0,6,24,60,840,15330,161616,1572984,29031120,636008670,

%T 11426850600,210095235636,5137568918664,139255673359530,

%U 3574532174656800,95923063388359920,2974073508961556256,98747639807081454774,3287535337205171488440

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

%F a(n) = n! * Sum_{k=0..floor(n/3)} k^(n-3*k) * binomial(n-2*k+1,k)/( (n-2*k+1)*(n-3*k)! ).

%o (PARI) a(n) = n!*sum(k=0, n\3, k^(n-3*k)*binomial(n-2*k+1, k)/((n-2*k+1)*(n-3*k)!));

%Y Cf. A370985, A371019, A371044, A371046.

%Y Cf. A365285.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Mar 09 2024