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

Author

Christian G. Bower, Jan 12 2004

Keywords

• nonn
• tabl
• changed

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).

Crossrefs

Cf. A029767, A091467.

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))).