A392829 E.g.f. A(x) satisfies A(x) = 1/(1 - x*log(1-x*A(x))^2).

1, 0, 0, 6, 24, 110, 2760, 39116, 485184, 10305144, 238592880, 5207444352, 135198201600, 4021267161600, 122974552698816, 4055791519461600, 147093555900211200, 5642681004581644800, 228580347898812789504, 9886264354137483765504, 451999533867513930777600

Offset

0,4

Links

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

Formula

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

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

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

Mathematica

Table[(n!/(n+1))* Sum[(2*k)!*Binomial[n+1, k]*Abs[StirlingS1[n-k, 2*k]]/(n-k)!, {k, 0, Floor[n/3]}], {n, 0, 21}] (* Vincenzo Librandi, Feb 06 2026 *)

Prog

(PARI) a(n) = n!*sum(k=0, n\3, (2*k)!*binomial(n+1, k)*abs(stirling(n-k, 2*k, 1))/(n-k)!)/(n+1);
(Magma) [(Factorial(n)/(n+1)) * &+[Factorial(2*k)* Binomial(n+1, k) * Abs(StirlingFirst(n - k, 2*k)) / Factorial(n - k): k in [0..Floor(n/3)]]: n in [0..25] ]; // Vincenzo Librandi, Feb 06 2026

Crossrefs

Cf. A392760.

Sequence in context: A392915 A392916 A392830 * A392760 A392856 A187668

Adjacent sequences: A392826 A392827 A392828 * A392830 A392831 A392832

Keyword

nonn

Author

Seiichi Manyama, Jan 24 2026

Status

approved