A002012 Almost trivalent maps.

4, 32, 200, 1120, 5880, 29568, 144144, 686400, 3208920, 14780480, 67251184, 302865472, 1352078000, 5990745600, 26369978400, 115407434880, 502503206040, 2178032472000, 9401840170800, 40434981787200, 173319035569680, 740642835229440, 3156148445580000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

References

• R. C. Mullin, E. Nemeth and P. J. Schellenberg, The enumeration of almost cubic maps, pp. 281-295 in Proceedings of the Louisiana Conference on Combinatorics, Graph Theory and Computer Science. Vol. 1, edited R. C. Mullin et al., 1970.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• A. M. Mathai and P. N. Rathie, Enumeration of almost cubic maps, Journal of Combinatorial Theory, Series B, Vol 13 (1972), 83-90.

Crossrefs

Cf. A002005, A002006, A002007, A002008, A002009, A002010, A002011.

Formula

a(n) = 2*(n+3)*(2*(n+1))! / (3*n!*(n+1)!). [Mathai & Rathie, Eq. (22)] - Andrey Zabolotskiy, Jun 24 2024

Extensions

Terms a(7) and beyond from Andrey Zabolotskiy, Jun 24 2024