A392935 E.g.f. A(x) satisfies A(x) = 1 - x^3*A(x)^5 * log(1 - x^2*A(x)^2).

1, 0, 0, 0, 0, 120, 0, 2520, 0, 120960, 25401600, 9979200, 3832012800, 1245404160, 719220902400, 91755151488000, 174356582400000, 45045272143872000, 53602095414067200, 21303098209096704000, 2012983121565351936000, 11213752210271170560000, 2291193190664226680832000

Offset

0,6

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

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

Mathematica

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 *)

Prog

(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))
(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

Crossrefs

Cf. A392932, A392934.

Sequence in context: A073836 A242836 A229031 * A392991 A392993 A221406

Adjacent sequences: A392932 A392933 A392934 * A392936 A392937 A392938

Keyword

nonn

Author

Seiichi Manyama, Jan 27 2026

Status

approved