A280759 Generalized Catalan triangle A_3 read by rows.

1, 1, 1, 1, 3, 3, 3, 2, 1, 12, 12, 12, 9, 6, 3, 1, 55, 55, 55, 43, 31, 19, 10, 4, 1, 273, 273, 273, 218, 163, 108, 65, 34, 15, 5, 1, 1428, 1428, 1428, 1155, 882, 609, 391, 228, 120, 55, 21, 6, 1, 7752, 7752, 7752, 6324, 4896, 3468, 2313, 1431, 822, 431, 203

Offset

0,5

Links

Lars Blomberg, Table of n, a(n) for n = 0..1599 (the first 40 rows)

Toufik Mansour, I. L. Ramirez, Enumerations of polyominoes determined by Fuss-Catalan words, Australas. J. Combin. 81 (3) (2021) 47-457

D. Merlini, R. Sprugnoli, M. C. Verri, The Tennis Ball Problem, J. Comb. Theory A 99 (2002) 307-344, Table 2

Sheng-Liang Yang, LJ Wang, Taylor expansions for the m-Catalan numbers, Australasian Journal of Combinatorics, Volume 64(3) (2016), Pages 420-431. Formula (5).

Example

Triangle begins:
     1,
     1,    1,    1,
     3,    3,    3,    2,   1,
    12,   12,   12,    9,   6,   3,   1,
    55,   55,   55,   43,  31,  19,  10,   4,   1,
   273,  273,  273,  218, 163, 108,  65,  34,  15,  5,  1,
  1428, 1428, 1428, 1155, 882, 609, 391, 228, 120, 55, 21, 6, 1,
  ...

Crossrefs

Cf. A001764 (row sums?), A062745 (rows reversed)

Sequence in context: A153012 A275300 A283833 * A016651 A135877 A136218

Adjacent sequences: A280756 A280757 A280758 * A280760 A280761 A280762

Keyword

nonn,tabf

Author

N. J. A. Sloane, Jan 16 2017

Extensions

More terms from Lars Blomberg, Jan 25 2017

Status

approved