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%I #15 Aug 09 2018 05:09:26
%S 1,2,20,512,25392,2093472,260555392,45819233280,10849051434240,
%T 3334632688448000,1292876470540099584,617862114722159788032,
%U 357118557050589336432640,245715466325821945360588800,198568949299946066906578944000,186309450278791634742517692366848
%N First column of triangular matrix A103244.
%H J.-B. Priez, A. Virmaux, <a href="http://arxiv.org/abs/1411.4161">Non-commutative Frobenius characteristic of generalized parking functions: Application to enumeration</a>, arXiv:1411.4161 [math.CO], 2014-2015.
%F For n>1: 0 = Sum_{k=1..n} C(n-1, k-1)*(-k^2-k)^(n-k)*a(k).
%t nmax = 16;
%t P = Table[If[n >= k, (-k^2-k)^(n-k)/(n-k)!, 0], {n, 1, nmax}, {k, 1, nmax}] // Inverse;
%t T[n_, k_] := If[n < k || k < 1, 0, P[[n, k]] (n - k)!];
%t a[n_] := T[n, 1];
%t Array[a, nmax] (* _Jean-François Alcover_, Aug 09 2018, from PARI *)
%o (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)!))}
%Y Cf. A103244.
%K nonn
%O 1,2
%A _Paul D. Hanna_, Feb 02 2005
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