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A103353 First column of triangular matrix A103244. 1
1, 2, 20, 512, 25392, 2093472, 260555392, 45819233280, 10849051434240, 3334632688448000, 1292876470540099584, 617862114722159788032, 357118557050589336432640, 245715466325821945360588800, 198568949299946066906578944000, 186309450278791634742517692366848 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 08:41 EST 2021. Contains 349627 sequences. (Running on oeis4.)