A392960 E.g.f. A(x) satisfies A(x) = 1 - (1/x^2) * log(1 - x^3*A(x)).

1, 1, 2, 6, 36, 300, 2880, 31920, 416640, 6289920, 106747200, 2005819200, 41453596800, 936076901760, 22923531671040, 604842984345600, 17107693508505600, 516496678400102400, 16579569163981824000, 563859651322314547200, 20253435671072507904000, 766203611728560445440000

Offset

0,3

Links

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

Formula

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

Mathematica

Table[n!* Sum[1/(k+1)! *Abs[StirlingS1[n-2*k, n-3*k]], {k, 0, Floor[n/3]}], {n, 0, 24}] (* Vincenzo Librandi, Feb 02 2026 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\3, 1/(k+1)!*abs(stirling(n-2*k, n-3*k, 1)));
(Magma) [Factorial(n)*&+[1/Factorial(k+1)* Abs(StirlingFirst(n-2*k, n-3*k)): k in [0..Floor(n/3)] ] : n in [0..24] ]; // Vincenzo Librandi, Feb 02 2026

Crossrefs

Cf. A138013, A392929.

Sequence in context: A234235 A277740 A392959 * A277393 A182037 A306066

Adjacent sequences: A392957 A392958 A392959 * A392961 A392962 A392963

Keyword

nonn

Author

Seiichi Manyama, Jan 28 2026

Status

approved