A103353 First column of triangular matrix A103244.

1, 2, 20, 512, 25392, 2093472, 260555392, 45819233280, 10849051434240, 3334632688448000, 1292876470540099584, 617862114722159788032, 357118557050589336432640, 245715466325821945360588800, 198568949299946066906578944000, 186309450278791634742517692366848

Offset: 1

Author

Paul D. Hanna, Feb 02 2005

Keywords

• nonn

Links

• J.-B. Priez, A. Virmaux, Non-commutative Frobenius characteristic of generalized parking functions: Application to enumeration, arXiv:1411.4161 [math.CO], 2014-2015.

Crossrefs

Cf. A103244.

Programs

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 *)

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)!))}

Formula

For n>1: 0 = Sum_{k=1..n} C(n-1, k-1)*(-k^2-k)^(n-k)*a(k).