A392933 - OEIS

%I #15 Jan 28 2026 03:08:26

%S 1,0,0,6,0,60,2160,1680,161280,4445280,16632000,1105695360,

%T 28740096000,284367283200,16330915560960,442998043488000,

%U 8416540945612800,454486527394099200,13751235468556185600,406476934064583782400,21668282110429194240000,759789627140273393664000

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

%H Vincenzo Librandi, <a href="/A392933/b392933.txt">Table of n, a(n) for n = 0..300</a>

%F E.g.f.: (1/x) * Series_Reversion( x/(1 - x*log(1-x^2)) ).

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

%t Table[(n!)^2 * Sum[1/(2*k+1)!*Abs[StirlingS1[k,n-2*k]/k!],{k,0,Floor[n/2]}],{n,0,20}] (* _Vincenzo Librandi_, Jan 28 2026 *)

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(1-x*log(1-x^2)))/x))

%o (Magma) [Factorial((n))^2* &+[1/Factorial(2*k+1) * Abs(StirlingFirst(k,n-2*k))/Factorial(k): k in [0..Floor(n/2)] ] : n in [0..23] ]; // _Vincenzo Librandi_, Jan 28 2026

%Y Cf. A376344, A392934.

%Y Cf. A371121, A392938.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Jan 27 2026