0,2

A. Brousseau, A sequence of power formulas, Fib. Quart., 6 (1968), 81-83.

A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 74.

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).

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.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

((4+n, 4)) (see A010048), or fibonomial(4+n, 4).

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).

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

A001656:=-1/(z-1)/(z**2-7*z+1)/(z**2+3*z+1); [Conjectured (correctly) by S. Plouffe in his 1992 dissertation.]

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]

Cf. A001654-5, A001657-8.

Sequence in context: A043019 A054604 A157794 this_sequence A087632 A124306 A124545

Adjacent sequences: A001653 A001654 A001655 this_sequence A001657 A001658 A001659

nonn,new

N. J. A. Sloane (njas(AT)research.att.com).

Corrected and extended by Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jun 27 2000

More terms and Mathematica program Vladimir Orlovsky (4vladimir(AT)gmail.com), Nov 23 2009