OFFSET
0,6
COMMENTS
A record in a word a_1,a_2,...,a_n is a letter a_j that is larger than all the preceding letters. That is, a_j>a_i for all i<j.
LINKS
Philippe Flajolet and Robert Sedgewick, Analytic Combinatorics, Cambridge Univ. Press, 2009.
FORMULA
G.f.: Product_{j=1..3} (1 + y*x/(1 - j*x)). Generally for words on alphabet {0,1,...,r} the o.g.f. is Product_{j=1..r} (1 + y*x/(1 - j*x)).
EXAMPLE
1, 0, 0, 0;
0, 3, 0, 0;
0, 6, 3, 0;
0, 14, 12, 1;
0, 36, 39, 6;
0, 98, 120, 25;
0, 276, 363, 90;
0, 794, 1092, 301;
0, 2316, 3279, 966;
MATHEMATICA
nn = 12; CoefficientList[Series[Product[1 + u z/(1 - j z), {j, 1, 3}], {z, 0, nn}], {z, u}] // Grid
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Geoffrey Critzer, Apr 27 2017
STATUS
approved