|
|
A243698
|
|
Number of meta-Sylvester classes of 4-multiparking functions of length n.
|
|
3
|
|
|
1, 1, 6, 65, 1014, 20598, 514604, 15240261, 521457190, 20226342858, 876527514436, 41952351066858, 2196985118015932, 124915413833339116, 7661168289958273560, 504025093269698008877, 35400246892564986253318, 2643280429851151580804610, 209058392585121976377752532
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
See Novelli-Thibon (2014) for precise definition.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 1/(1-x) = Sum_{n>=0} a(n) * x^n*(1-x)^n / Product_{k=1..n} (1 + 4*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 + 4j x + x O[x]^n, {j, 0, k}], {k, 1, n-1}], x, n]];
|
|
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+4*j*x+x*O(x^n))), n))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|