A091466 Table (by antidiagonals) of labeled alternating octopuses with n black nodes and k white nodes. Each type of object labeled from its own label set.
1, 2, 2, 0, 14, 0, 0, 36, 36, 0, 0, 24, 336, 24, 0, 0, 0, 1296, 1296, 0, 0, 0, 0, 2160, 14832, 2160, 0, 0, 0, 0, 1440, 80640, 80640, 1440, 0, 0, 0, 0, 0, 233280, 1082880, 233280, 0, 0, 0, 0, 0, 0, 362880, 7776000, 7776000, 362880, 0, 0, 0, 0, 0, 0, 241920, 33264000
Offset: 1
Examples
1 2 0 0 0 ... 2 4 36 24 0 ... 0 36 336 1296 2160 ... 0 24 1296 14832 80640 ... 0 0 2160 80640 1082880 ...
References
- F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, p. 113 (2.4.41).
Formula
Double e.g.f.: A(x, y) = Sum_{i, j>=0} (x^i*y^j/(i!*j!)) = log((1-x*y)^2/(1-x*y*(3+x+y))).