A001660 Hypotenusal numbers.

1, 1, 2, 6, 36, 876, 408696, 83762796636, 3508125906207095591916, 6153473687096578758445014683368786661634996, 18932619208894981833333582059033329370801260096062214926751788496235698477988081702676

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• nice

References

• 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).
• J. J. Sylvester and M. J. Hammond, On Hamilton's numbers, Phil. Trans. Roy. Soc., 178 (1887), 285-312.

Links

• E. Lucas, Théorie des Nombres, Gauthier-Villars, Paris, 1891, Vol. 1, p. 496.
• E. Lucas, Théorie des Nombres, Gauthier-Villars, Paris, 1891, Vol. 1. [Annotated scan of pages 488-499 only]

Crossrefs

First differences of A000905.

Programs

Mathematica

h[1] = 2; h[n_] := h[n] = 2+Sum[(-1)^(i+1)*Product[h[n-i]-k, {k, 0, i}]/(i+1)!, {i, 1, n-1}]; a[0] = 1; a[n_] := h[n+1] - h[n]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Dec 05 2013 *)