%I A001656 M3989 N1653
%S A001656 1,5,40,260,1820,12376,85085,582505,3994320,27372840,187628376,
%T A001656 1285992240,8814405145,60414613805,414088493560,2838203264876,
%U A001656 19453338487220,133335155341960,913892777190965,6263914210945105
%N A001656 Fibonomial coefficients.
%D A001656 A. Brousseau, A sequence of power formulas, Fib. Quart., 6 (1968), 81-83.
%D A001656 A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci 
               Association, San Jose, CA, 1972, p. 74.
%D A001656 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001656 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001656 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">
               Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures</
               a>, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%H A001656 S. Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">
               1031 Generating Functions and Conjectures</a>, Universit\'{e} du 
               Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
%F A001656 ((4+n, 4)) (see A010048), or fibonomial(4+n, 4).
%F A001656 G.f.: 1/(1-5*x-15*x^2+15*x^3+5*x^4-x^5) = 1/((1-x)*(1+3*x+x^2)*(1-7*x+x^2)) 
               (see Comments to A055870). a(n)= 7*a(n-1)-a(n-2)+((-1)^n)*fibonomial(n+2, 
               2), n >= 2; a(0)=1, a(1)=5; fibonomial(n+2, 2)= A001654(n+1).
%p A001656 with (combinat): a:=n->1/6*fibonacci(n)*fibonacci(n+1)*fibonacci(n+2)*fibonacci(n+3): 
               seq(a(n), n=1..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Oct 07 2007
%p A001656 A001656:=-1/(z-1)/(z**2-7*z+1)/(z**2+3*z+1); [Conjectured (correctly) 
               by S. Plouffe in his 1992 dissertation.]
%t A001656 Table[(Fibonacci[n+3]*Fibonacci[n+2]*Fibonacci[n+1]*Fibonacci[n])/6,{n,
               0,50}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 23 2009]
%Y A001656 Cf. A001654-5, A001657-8.
%Y A001656 Sequence in context: A043019 A054604 A157794 this_sequence A087632 A124306 
               A124545
%Y A001656 Adjacent sequences: A001653 A001654 A001655 this_sequence A001657 A001658 
               A001659
%K A001656 nonn,new
%O A001656 0,2
%A A001656 N. J. A. Sloane (njas(AT)research.att.com).
%E A001656 Corrected and extended by Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), 
               Jun 27 2000
%E A001656 More terms and Mathematica program Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Nov 23 2009