A243696 Number of meta-Sylvester classes of 2-multiparking functions of length n.

1, 1, 4, 27, 254, 3048, 44328, 755681, 14750646, 323999500, 7901623624, 211690439030, 6176393964684, 194847458672328, 6606138879434128, 239466033046020357, 9239284257332493478, 377948418993992417644, 16335430070738649950536, 743711790322786003051882

Offset

0,3

Comments

See Novelli-Thibon (2014) for precise definition.

Sum over all Dyck paths of semilength n of products over all peaks p of (1+x_p-y_p), where x_p and y_p are the coordinates of peak p. - Alois P. Heinz, May 27 2015

Links

Alois P. Heinz, Table of n, a(n) for n = 0..400

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 + 2*k*x). - Paul D. Hanna, Jun 14 2014

Maple

b:= proc(x, y, t) option remember; `if`(y>x or y<0, 0,
      `if`(x=0, 1, b(x-1, y-1, false)*`if`(t, (1+x-y), 1) +
                   b(x-1, y+1, true)))
    end:
a:= n-> b(2*n, 0, false):
seq(a(n), n=0..25);  # Alois P. Heinz, May 27 2015

Mathematica

b[x_, y_, t_] := b[x, y, t] = If[y>x || y<0, 0, If[x==0, 1, b[x-1, y-1, False]*If[t, 1+x-y, 1] + b[x-1, y+1, True]]]; a[n_] := b[2*n, 0, False]; Table[a[n], {n, 0, 25}] (* Jean-François Alcover, Feb 24 2016, after Alois P. Heinz *)

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+2*j*x+x*O(x^n))), n))}
for(n=0, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Jun 14 2014

Crossrefs

Cf. A132624, A243697, A243698, A243699.

Sequence in context: A201996 A239368 A245408 * A158836 A350276 A350275

Adjacent sequences: A243693 A243694 A243695 * A243697 A243698 A243699

Keyword

nonn

Author

N. J. A. Sloane, Jun 14 2014

Extensions

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

Status

approved