|
| |
|
|
A001656
|
|
Fibonomial coefficients.
(Formerly M3989 N1653)
|
|
4
| |
|
|
1, 5, 40, 260, 1820, 12376, 85085, 582505, 3994320, 27372840, 187628376, 1285992240, 8814405145, 60414613805, 414088493560, 2838203264876, 19453338487220, 133335155341960, 913892777190965, 6263914210945105
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
REFERENCES
| 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).
|
|
|
LINKS
| 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.
Index to sequences with linear recurrences with constant coefficients, signature (5,15,-15,-5,1).
|
|
|
FORMULA
| ((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).
a(n)=product(Fibonacci(k+4)/Fibonacci(k), k=1..n) [From Gary Detlefs, Feb 06 2011]
a(n)=(F(n+3)^2-F(n+2)^2)*F(n+3)*F(n+2)/6, where F(n) is the n-th Fibonacci number.[From Gary Detlefs, Oct 12 2011]
|
|
|
MAPLE
| 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.]
|
|
|
MATHEMATICA
| 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]
|
|
|
CROSSREFS
| Cf. A001654-5, A001657-8.
Sequence in context: A043019 A054604 A157794 * A087632 A124306 A124545
Adjacent sequences: A001653 A001654 A001655 * A001657 A001658 A001659
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| 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
|
| |
|
|
