A103353 First column of triangular matrix A103244.

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

Offset

1,2

Links

Table of n, a(n) for n=1..16.

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

Cf. A103244.

Sequence in context: A277414 A296789 A168136 * A009344 A009699 A101927

Adjacent sequences: A103350 A103351 A103352 * A103354 A103355 A103356

Keyword

nonn

Author

Paul D. Hanna, Feb 02 2005

Status

approved