A094100 Fit a polynomial of degree k-1 to column k of array in A048790, evaluate it at dimension n = -1.

1, -2, 9, -64, 560, -5370, 53788, -555864, 5957685, -66459200, 763983132, -8919566196, 105678848821, -1286858544734

Offset: 1

Author

Dan Hoey

Keywords

• sign
• more

Comments

Might be thought of as number of rooted (-1)-dimensional "polycubes" with n cells, with no symmetries removed.

References

• Dan Hoey, Bill Gosper and Richard C. Schroeppel, Discussions in Math-Fun Mailing list, circa Jul 13 1999.

Links

• Sebastian Luther and Stephan Mertens, Counting lattice animals in high dimensions, Journal of Statistical Mechanics: Theory and Experiment, 2011 (9), 546-565; arXiv:1106.1078 [cond-mat.stat-mech], 2011.
• R. C. Schroeppel, A few mathematical experiments

Crossrefs

Cf. A094101, A048663-A048868.

Extensions

a(9)-a(14) using Luther & Mertens's formulas added by Andrei Zabolotskii, Jun 27 2025