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 A034802 Triangle of Fibonomial coefficients (k=3). 2
 1, 1, 1, 1, 4, 1, 1, 17, 17, 1, 1, 72, 306, 72, 1, 1, 305, 5490, 5490, 305, 1, 1, 1292, 98515, 417240, 98515, 1292, 1, 1, 5473, 1767779, 31716035, 31716035, 1767779, 5473, 1, 1, 23184, 31721508, 2410834608, 10212563270, 2410834608, 31721508, 23184, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 REFERENCES A. Brousseau, Fibonacci and Related Number Theoretic Tables. Fibonacci Association, San Jose, CA, 1972, p. 88. LINKS G. C. Greubel, Rows n = 0..75 of triangle, flattened C. Pita, On s-Fibonomials, J. Int. Seq. 14 (2011) # 11.3.7. FORMULA T(n, k) = Product_{j=0..k-1} Fibonacci(3*(n-j))/Product_{j=1..k} Fibonacci(3*j). Fibonomial coefficients formed from sequence F_4k [ 3 21 144 987 ... ]. MATHEMATICA F[n_, k_, q_]:= Product[Fibonacci[q*(n-j+1)]/Fibonacci[q*j], {j, k}]; Table[F[n, k, 3], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 13 2019 *) PROG (PARI) F(n, k, q) = f=fibonacci; prod(j=1, k, f(q*(n-j+1))/f(q*j)); \\ G. C. Greubel, Nov 13 2019 (Sage) def F(n, k, q):     if (n==0 and k==0): return 1     else: return product(fibonacci(q*(n-j+1))/fibonacci(q*j) for j in (1..k)) [[F(n, k, 3) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Nov 13 2019 (GAP) F:= function(n, k, q)     if n=0 and k=0 then return 1;     else return Product([1..k], j-> Fibonacci(q*(n-j+1))/Fibonacci(q*j));     fi;   end; Flat(List([0..10], n-> List([0..n], k-> F(n, k, 3) ))); # G. C. Greubel, Nov 13 2019 CROSSREFS Cf. A010048. Sequence in context: A174639 A173814 A176467 * A177262 A203092 A139167 Adjacent sequences:  A034799 A034800 A034801 * A034803 A034804 A034805 KEYWORD nonn,tabl AUTHOR EXTENSIONS More terms from James A. Sellers, Feb 09 2000 Terms of 8th row corrected by Georg Fischer, Dec 01 2019 STATUS approved

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Last modified December 4 12:55 EST 2021. Contains 349525 sequences. (Running on oeis4.)