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%I #17 Jul 27 2018 04:39:49
%S 1,1,5,44,551,8919,176634,4130208,111222029,3386390387,114938069867,
%T 4300300340056,175745611297708,7786523264786248,371635506967477674,
%U 19004259907335519264,1036363461255181310601,60024383356961580954471,3679068900776781256346115
%N Number of meta-Sylvester classes of 3-multiparking functions of length n.
%C See Novelli-Thibon (2014) for precise definition.
%H J.-C. Novelli, J.-Y. Thibon, <a href="http://arxiv.org/abs/1403.5962">Hopf Algebras of m-permutations, (m+1)-ary trees, and m-parking functions</a>, arXiv preprint arXiv:1403.5962 [math.CO], 2014. See Fig. 28.
%F G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n*(1-x)^n / Product_{k=1..n} (1 + 3*k*x). - _Paul D. Hanna_, Jun 14 2014
%t a[n_] := a[n] = If[n<0, 0, Coefficient[1/(1 - x + x O[x]^n) - Sum[a[k] x^k (1-x)^k/Product[1 + 3j x + x O[x]^n, {j, 0, k}], {k, 1, n-1}], x, n]];
%t Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, Jul 27 2018, from PARI *)
%o (PARI) {a(n)=if(n<0, 0, polcoeff(1/(1-x+x*O(x^n)) - sum(k=1, n-1, a(k)*x^k*(1-x)^k/prod(j=0, k, 1+3*j*x+x*O(x^n))), n))}
%o for(n=0, 20, print1(a(n), ", ")) \\ _Paul D. Hanna_, Jun 14 2014
%Y Cf. A132624, A243696, A243698, A243699.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jun 14 2014
%E Offset changed to 0 by _Paul D. Hanna_, Jun 14 2014
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