OFFSET
1,2
LINKS
J.-B. Priez, A. Virmaux, Non-commutative Frobenius characteristic of generalized parking functions: Application to enumeration, arXiv:1411.4161 [math.CO], 2014-2015.
FORMULA
For n>1: 0 = Sum_{k=1..n} C(n-1, k-1)*(-k^2-k)^(n-k)*a(k).
MATHEMATICA
nmax = 16;
P = Table[If[n >= k, (-k^2-k)^(n-k)/(n-k)!, 0], {n, 1, nmax}, {k, 1, nmax}] // Inverse;
T[n_, k_] := If[n < k || k < 1, 0, P[[n, k]] (n - k)!];
a[n_] := T[n, 1];
Array[a, nmax] (* Jean-François Alcover, Aug 09 2018, from PARI *)
PROG
(PARI) {a(n)=local(P); if(n>=1, P=matrix(n, n, r, c, if(r>=c, (-c^2-c)^(r-c)/(r-c)!))); return(if(n<1, 0, (P^-1)[n, 1]*(n-1)!))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Feb 02 2005
STATUS
approved