A392935 - OEIS

%I #15 Feb 02 2026 22:28:41

%S 1,0,0,0,0,120,0,2520,0,120960,25401600,9979200,3832012800,1245404160,

%T 719220902400,91755151488000,174356582400000,45045272143872000,

%U 53602095414067200,21303098209096704000,2012983121565351936000,11213752210271170560000,2291193190664226680832000

%N E.g.f. A(x) satisfies A(x) = 1 - x^3*A(x)^5 * log(1 - x^2*A(x)^2).

%H Vincenzo Librandi, <a href="/A392935/b392935.txt">Table of n, a(n) for n = 0..300</a>

%F E.g.f.: (1/x) * Series_Reversion( x * (1 + sqrt(1 + 4*x^3*log(1-x^2)))/2 ).

%t Nmax=23; f=Series[x*(1+Sqrt[1+4 x^3 Log[1-x^2]])/2,{x,0,Nmax+5}]; g=InverseSeries[f]/x; Table[Factorial[n]*Coefficient[g,x,n],{n,0,Nmax}] (* _Vincenzo Librandi_, Jan 28 2026 *)

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+sqrt(1+4*x^3*log(1-x^2)))/2)/x))

%o (Magma) N := 25; R<x> := PowerSeriesRing(Rationals(), N+1); A := 1 + O(x); for i in [1..N] do A := 1 - x^3 * A^5 * Log(1 - x^2 * A^2); end for; n := [ Factorial(n) * Coefficient(A, n): n in [0..N] ]; n; // _Vincenzo Librandi_, Jan 28 2026

%Y Cf. A392932, A392934.

%K nonn

%O 0,6

%A _Seiichi Manyama_, Jan 27 2026