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A005363 Hoggatt sequence.
(Formerly M1867)
4

%I M1867

%S 1,2,8,44,310,2606,25202,272582,3233738,41454272,567709144,8230728508,

%T 125413517530,1996446632130,33039704641922,566087847780250,

%U 10006446665899330,181938461947322284,3393890553702212368,64807885247524512668,1264344439859632559216

%N Hoggatt sequence.

%D D. C. Fielder and C. O. Alford, ``An investigation of sequences derived from Hoggatt sums and Hoggatt triangles,'' in G. E. Bergum et al., editors, Applications of Fibonacci Numbers: Proc. Third Internat. Conf. on Fibonacci Numbers and Their Applications, Pisa, Jul 25-29, 1988. Kluwer, Dordrecht, Vol. 3, 1990, pp. 77-88.

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

%H D. C. Fielder, <a href="/A005362/a005362.pdf">Letter to N. J. A. Sloane, Jun 1988</a>

%H D. C. Fielder and C. O. Alford, <a href="http://www.fq.math.ca/Scanned/27-2/fielder.pdf">On a conjecture by Hoggatt with extensions to Hoggatt sums and Hoggatt triangles</a>, Fib. Quart., 27 (1989), 160-168.

%H D. C. Fielder & C. O. Alford, <a href="/A000108/a000108_19.pdf">An investigation of sequences derived from Hoggatt Sums and Hoggatt Triangles</a>, Application of Fibonacci Numbers, 3 (1990) 77-88. Proceedings of 'The Third Annual Conference on Fibonacci Numbers and Their Applications,' Pisa, Italy, July 25-29, 1988. (Annotated scanned copy)

%F (n+4)(n+5)^2(n+6)(n+7)(n+8)(252+253n+55n^2)a(n) = 3(n+4)(n+5) (141120 +362152n+373054n^2+192647n^3+52441n^4+7161n^5+385n^6)a(n-1) + n(n-1)(5738880+14311976n+14466242n^2+7579175n^3+2170343n^4 +322289n^5 +19415n^6) a(n-2) - 32(n-1)^2 n^2(n-2)(n+1)(560 + 363n + 55n^2)a(n-3); a(-1)=a(0)=1, a(1)=2 - Richard L. Ollerton (r.ollerton(AT)uws.edu.au), Sep 12 2006

%F a(n) = S(5,n) where S(d,n) is defined in A005364. - _Sean A. Irvine_, May 29 2016

%t A005363[n_]:=HypergeometricPFQ[{-4-n,-3-n,-2-n,-1-n,-n},{2,3,4,5},-1] (* Richard L. Ollerton (r.ollerton(AT)uws.edu.au), Sep 12 2006 *)

%Y Cf. A005364.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, _Simon Plouffe_

%E More terms from _Sean A. Irvine_, May 29 2016

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Last modified June 25 07:53 EDT 2019. Contains 324347 sequences. (Running on oeis4.)