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Hypotenusal numbers.
(Formerly M1706 N0675)
1

%I M1706 N0675 #23 Oct 12 2015 23:05:16

%S 1,1,2,6,36,876,408696,83762796636,3508125906207095591916,

%T 6153473687096578758445014683368786661634996,

%U 18932619208894981833333582059033329370801260096062214926751788496235698477988081702676

%N Hypotenusal numbers.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

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

%H E. Lucas, <a href="http://gallica.bnf.fr/ark:/12148/bpt6k29021h">Théorie des Nombres</a>, Gauthier-Villars, Paris, 1891, Vol. 1, p. 496.

%H E. Lucas, <a href="/A000904/a000904.pdf">Théorie des Nombres</a>, Gauthier-Villars, Paris, 1891, Vol. 1. [Annotated scan of pages 488-499 only]

%t 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 *)

%Y First differences of A000905.

%K nonn,easy,nice

%O 0,3

%A _N. J. A. Sloane_