A243697 Number of meta-Sylvester classes of 3-multiparking functions of length n.

1, 1, 5, 44, 551, 8919, 176634, 4130208, 111222029, 3386390387, 114938069867, 4300300340056, 175745611297708, 7786523264786248, 371635506967477674, 19004259907335519264, 1036363461255181310601, 60024383356961580954471, 3679068900776781256346115

Offset

0,3

Comments

See Novelli-Thibon (2014) for precise definition.

Links

Table of n, a(n) for n=0..18.

J.-C. Novelli, J.-Y. Thibon, Hopf Algebras of m-permutations, (m+1)-ary trees, and m-parking functions, arXiv preprint arXiv:1403.5962 [math.CO], 2014. See Fig. 28.

Formula

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

Mathematica

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]];
Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Jul 27 2018, from PARI *)

Prog

(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))}
for(n=0, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Jun 14 2014

Crossrefs

Cf. A132624, A243696, A243698, A243699.

Sequence in context: A249791 A215648 A195242 * A106273 A349836 A052803

Adjacent sequences: A243694 A243695 A243696 * A243698 A243699 A243700

Keyword

nonn

Author

N. J. A. Sloane, Jun 14 2014

Extensions

Offset changed to 0 by Paul D. Hanna, Jun 14 2014

Status

approved