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A001658
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Fibonomial coefficients.
(Formerly M4919 N2112)
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4
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1, 13, 273, 4641, 85085, 1514513, 27261234, 488605194, 8771626578, 157373300370, 2824135408458, 50675778059634, 909348684070099, 16317540120588343, 292806787575013635, 5254201798026392211, 94282845030238533383
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| The thirteen listed terms satisfy the linear recurrence a(n) = 13a(n - 1) + 104a(n - 2) - 260a(n - 3) - 260a(n - 4) + 104a(n - 5) + 13a(n - 6) - a(n - 7) for n>6 - John W. Layman (layman(AT)math.vt.edu), Apr 14 2000
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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).
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FORMULA
| G.f.: 1/(1-13*x-104*x^2+260*x^3+260*x^4-104*x^5-13*x^6+x^7) = 1/((1+x)*(1-3*x+x^2)*(1+7*x+x^2)*(1-18*x+x^2)) (see Comments to A055870).
a(n) = 5*a(n-1)+F(n-5)*Fibonomial(n+5, 5), n >= 1, a(0) = 1; F(n) = A000045(n) (Fibonacci). a(n) = 18*a(n-1)-a(n-2)+((-1)^n)*Fibonomial(n+4, 4), n >= 2; a(0) = 1, a(1) = 13; Fibonomial(n+4, 4) = A001656(n).
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MAPLE
| with(combinat):a:=n->1/240*fibonacci(n)*fibonacci(n+1)*fibonacci(n+2)*fibonacci(n+3)*fibonacci(n+4)*fibonacci(n+5): seq(a(n), n=1..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 07 2007
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MATHEMATICA
| f[n_]:=Fibonacci[n]*Fibonacci[n+1]*Fibonacci[n+2]*Fibonacci[n+3]*Fibonacci[n+4]*Fibonacci[n+5]; lst={}; Do[AppendTo[lst, f[n]/240], {n, 0, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 12 2010]
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CROSSREFS
| Sequence in context: A142262 A163155 A183515 * A034911 A196652 A197455
Adjacent sequences: A001655 A001656 A001657 * A001659 A001660 A001661
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms and formulae from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Jul 13 200, who also observes that Layman's recurrence is indeed true for all n >= 7.
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