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A001660

Hypotenusal numbers.
(Formerly M1706 N0675)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

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

Table of n, a(n) for n=0..10.

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]

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 *)

CROSSREFS

First differences of A000905.

Sequence in context: A208650 A374453 A152480 * A368139 A275904 A014052

Adjacent sequences: A001657 A001658 A001659 * A001661 A001662 A001663

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane

STATUS

approved