OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..1000
Nickolas Hein and Jia Huang, Modular Catalan Numbers, arXiv:1508.01688 [math.CO], 2015.
Nickolas Hein and Jia Huang, Modular Catalan Numbers, European Journal of Combinatorics 61 (2017), 197-218.
L. Takacs, Enumeration of rooted trees and forests, Math. Scientist 18 (1993), 1-10, esp. Eq. (6).
FORMULA
G.f. A(x) satisfies: A(x) = 1 + Sum_{k=1..7} x^k*A(x)^k. - Ilya Gutkovskiy, May 03 2019
MAPLE
r := 7; [ seq((1/n)*add( (-1)^j*binomial(n, j)*binomial(2*n-2-j*(r+1), n-1), j=0..floor((n-1)/(r+1))), n=1..30) ];
# second Maple program:
b:= proc(u, o) option remember; `if`(u+o=0, 1,
add(b(u-j, o+j-1), j=1..min(1, u))+
add(b(u+j-1, o-j), j=1..min(7, o)))
end:
a:= n-> b(0, n):
seq(a(n), n=0..30); # Alois P. Heinz, Aug 28 2017
MATHEMATICA
b[u_, o_] := b[u, o] = If[u + o == 0, 1, Sum[b[u - j, o + j - 1], {j, 1, Min[1, u]}] + Sum[b[u + j - 1, o - j], {j, 1, Min[7, o]}]];
a[n_] := b[0, n];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Oct 27 2017, after Alois P. Heinz *)
PROG
(PARI) a(n)=if(n<0, 0, polcoeff(serreverse(x/sum(k=0, 7, x^k)+O(x^(n+2))), n+1)) /* Ralf Stephan */
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Name clarified by Andrew Howroyd, Dec 04 2017
STATUS
approved