%I A001655 M2988 N1208
%S A001655 1,3,15,60,260,1092,4641,19635,83215,352440,1493064,6324552,
%T A001655 26791505,113490195,480752895,2036500788,8626757644,36543528780,
%U A001655 154800876945,655747029795,2777789007071,11766903040368,49845401197200
%N A001655 Fibonomial coefficients: F(n)F(n+1)F(n+2)/2, where F() = Fibonacci numbers 
               A000045.
%D A001655 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A001655 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001655 S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques 
               Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 
               1992.
%D A001655 A. Brousseau, A sequence of power formulas, Fib. Quart., 6 (1968), 81-83.
%D A001655 A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci 
               Association, San Jose, CA, 1972, p. 74.
%H A001655 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 A001655 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 A001655 G.f.: (1 + x - x^2 )^-1 (1 - 4x - x^2 )^-1.
%F A001655 G.f.: 1/(1-3*x-6*x^2+3*x^3+x^4) = 1/((1+x-x^2)*(1-4*x-x^2)) (see Comments 
               to A055870). a(n)=A010048(n+3, 3)= fibonomial(n+3, 3). Recursion: 
               a(n)= 4*a(n-1)+a(n-2)+((-1)^n)*F(n+1), n >= 2; a(0)=1, a(1)=3.
%p A001655 A001655:=1/(z**2-z-1)/(z**2+4*z-1); [Conjectured by S. Plouffe in his 
               1992 dissertation.]
%t A001655 Table[(Fibonacci[n+2]*Fibonacci[n+1]*Fibonacci[n])/2,{n,0,40}] [From 
               Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 23 2009]
%Y A001655 Equals 1/2 * A065563(n).
%Y A001655 First differences are in A066258.
%Y A001655 Sequence in context: A036750 A058748 A049314 this_sequence A128237 A058749 
               A072336
%Y A001655 Adjacent sequences: A001652 A001653 A001654 this_sequence A001656 A001657 
               A001658
%K A001655 nonn,easy,new
%O A001655 0,2
%A A001655 N. J. A. Sloane (njas(AT)research.att.com).