A371230 - OEIS

%I #14 Sep 04 2025 14:55:53

%S 1,0,2,3,128,750,29964,377160,15795072,329631120,15001287120,

%T 449174341440,22551082739712,885381886509120,49302509206648320,

%U 2391802812599316480,147728974730632012800,8502972330919072688640,580806950108814502345728

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

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

%t terms=19; A[_]=1; Do[A[x_]= 1 - x*A[x]^3*Log[1 - x*A[x]^2] + O[x]^terms//Normal, terms]; CoefficientList[Series[A[x],{x,0,terms}],x]*Range[0,terms-1]! (* _Stefano Spezia_, Sep 03 2025 *)

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

%Y Cf. A371227, A371228, A371229.

%Y Cf. A370993, A371232.

%Y Cf. A371122.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Mar 15 2024