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Revision History for A056566

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A056566

Fibonomial coefficients.
(history; published version)

#27 by Bruno Berselli at Mon May 09 02:57:59 EDT 2016

STATUS

reviewed

approved

#26 by Vaclav Kotesovec at Mon May 09 01:43:12 EDT 2016

STATUS

proposed

reviewed

#25 by Giovanni Resta at Sun May 08 04:44:05 EDT 2016

STATUS

editing

proposed

Discussion

Sun May 08

05:55

Joerg Arndt: Similar (fugly) programs in my current edits should IMHO also be removed.

#24 by Giovanni Resta at Sun May 08 04:42:35 EDT 2016

MATHEMATICA

f[n_]:=Fibonacci[n]*Fibonacci[n+1]*Fibonacci[n+2] *Fibonacci[n+3] *Fibonacci[n+4] *Fibonacci[n+5]*Fibonacci[n+6]*Fibonacci[n+7]; lst={}; Do[AppendTo[lst, f[n]/65520], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 12 2010 *)

a[n_] := (1/65520) Times @@ Fibonacci[n + Range[8]]; Array[a, 20, 0] (* Giovanni Resta, May 08 2016 *)

STATUS

proposed

editing

Discussion

Sun May 08

04:43

Giovanni Resta: I replaced the old Mma program because (1) it produced 0,1,34,... (2) it was ugly.

#23 by Michel Marcus at Sun May 08 04:29:37 EDT 2016

STATUS

editing

proposed

#22 by Michel Marcus at Sun May 08 04:29:31 EDT 2016

FORMULA

a(n) = A010048(n+8, 8) =: Fibonomial(n+8, 8).

G.f. : 1/p(9, n) with p(9, n)= 1 - 34*x - 714*x^2 + 4641*x^3 + 12376*x^4 - 12376*x^5 - 4641*x^6 + 714*x^7 + 34*x^8 - x^9 = (1-x)*(1 + 3*x + x^2)*(1 - 7*x + x^2)* (1 + 18*x + x^2)*(1 - 47*x + x^2) (n=9 row polynomial of signed Fibonomial triangle A055870; see this entry for Knuth and Riordan references).

STATUS

proposed

editing

#21 by Joerg Arndt at Sun May 08 04:16:08 EDT 2016

STATUS

editing

proposed

#20 by Joerg Arndt at Sun May 08 04:16:02 EDT 2016

PROG

(PARI) b(n, k)=prod(j=1, k, fibonacci(n+j)/fibonacci(j)); \\ fibonomial coefficients

STATUS

proposed

editing

#19 by Joerg Arndt at Sun May 08 04:08:36 EDT 2016

STATUS

editing

proposed

#18 by Joerg Arndt at Sun May 08 04:08:29 EDT 2016

PROG

(PARI) b(n, k)=prod(j=1, k, fibonacci(n+j)/fibonacci(j)); \\ fibonomial coefficients

vector(20, n, b(n-1, 8)) \\ Joerg Arndt, May 08 2016

STATUS

approved

editing