OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..400
FORMULA
E.g.f.: -LambertW(-x^3 * (1+x))/x^3.
E.g.f.: (1+x) * exp( -LambertW(-x^3 * (1+x)) ).
a(n) = n! * Sum_{k=0..floor(n/3)} (k+1)^(k-1) * binomial(k+1,n-3*k)/k!.
MATHEMATICA
Table[n!*Sum[(k+1)^(k-1)*Binomial[k+1, n-3*k]/k!, {k, 0, Floor[n/3]}], {n, 0, 25}] (* Vincenzo Librandi, Nov 01 2025 *)
PROG
(PARI) a(n) = n!*sum(k=0, n\3, (k+1)^(k-1)*binomial(k+1, n-3*k)/k!);
(Magma) [Factorial(n) * &+[(k+1)^(k-1)* Binomial(k+1, n-3*k) / Factorial(k) : k in [0..Floor(n/3)]] : n in [0..25] ]; // Vincenzo Librandi, Nov 01 2025
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Oct 16 2025
STATUS
approved
