A356970 - OEIS

%I #10 Sep 12 2022 03:05:37

%S 1,0,0,6,12,40,1980,16128,136080,4224960,70943040,1087178400,

%T 31274100000,784834652160,18115033128192,565994928945600,

%U 18161466717139200,560655551681971200,20108422243585658880,769928646324249699840,29464638272901949824000

%N E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^2 * A(x)).

%F a(n) = n! * Sum_{k=0..floor(n/3)} (n-k+1)^(k-1) * |Stirling1(n-2*k,k)|/(n-2*k)!.

%t m = 21; (* number of terms *)

%t A[_] = 0;

%t Do[A[x_] = 1/(1 - x*A[x])^(x^2*A[x]) + O[x]^m // Normal, {m}];

%t CoefficientList[A[x], x]*Range[0, m - 1]! (* _Jean-François Alcover_, Sep 12 2022 *)

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

%Y Cf. A184949, A349556, A356971.

%Y Cf. A356967.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Sep 07 2022