|
| |
|
|
A047812
|
|
Parker's partition triangle read by rows.
|
|
12
| |
|
|
1, 1, 1, 1, 3, 1, 1, 5, 7, 1, 1, 9, 20, 11, 1, 1, 13, 48, 51, 18, 1, 1, 20, 100, 169, 112, 26, 1, 1, 28, 194, 461, 486, 221, 38, 1, 1, 40, 352, 1128, 1667, 1210, 411, 52, 1, 1, 54, 615, 2517, 4959, 5095, 2761, 720, 73, 1, 1, 75, 1034, 5288, 13241, 18084, 13894, 5850
(list; table; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,5
|
|
|
COMMENTS
| The entries in row n are the coefficients of q^(k(n+1)) in the q-binomial coefficient [2n,n] where k runs from 0 to n-1 - James A. Sellers (sellersj(AT)math.psu.edu).
|
|
|
REFERENCES
| R. K. Guy, Parker's permutation problem involves the Catalan numbers, Amer. Math. Monthly 100 (1993), 287-289.
|
|
|
EXAMPLE
| 1; 1 1; 1 3 1; 1 5 7 1; ...
|
|
|
MATHEMATICA
| s[n_] := s[n] = Series[ Product[(1-q^(2n-k)) / (1-q^(k+1)), {k, 0, n-1}], {q, 0, n^2}]; t[n_, k_] := SeriesCoefficient[ s[n], k(n+1)]; Flatten[ Table[ t[n, k], {n, 0, 11}, {k, 0, n-1}]] (* From Jean-François Alcover, Jan 27 2012 *)
|
|
|
CROSSREFS
| Sequence in context: A119258 A099608 A047969 * A129392 A118538 A141523
Adjacent sequences: A047809 A047810 A047811 * A047813 A047814 A047815
|
|
|
KEYWORD
| nonn,tabl,easy,nice
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from James A. Sellers (sellersj(AT)math.psu.edu)
|
| |
|
|
