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 A173890 Triangle T(n, k) = c(n)/(c(k)*c(n-k)) where c(n) = (n-2)!*(n-1)!*n!*(n+1)!*(n+3)!/1440 with c(0) = c(1) = 1 and c(2) = 2, read by rows. 2
 1, 1, 1, 1, 2, 1, 1, 72, 72, 1, 1, 840, 30240, 840, 1, 1, 2880, 1209600, 1209600, 2880, 1, 1, 7560, 10886400, 127008000, 10886400, 7560, 1, 1, 16800, 63504000, 2540160000, 2540160000, 63504000, 16800, 1, 1, 33264, 279417600, 29338848000, 100590336000, 29338848000, 279417600, 33264, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n, k) = c(n)/(c(k)*c(n-k)) where c(n) = (n-2)!*(n-1)!*n!*(n+1)!*(n+3)!/1440 with c(0) = c(1) = 1 and c(2) = 2. T(n, k) = c(n)/(c(k)*c(n-k)) where c(n) = Product_{j=3..n} (j-2)*(j-1)*(j)*(j+1)*(j+3) with c(0) = c(1) = 1 and c(2) = 2. EXAMPLE The triangle begins as: 1; 1, 1; 1, 2, 1; 1, 72, 72, 1; 1, 840, 30240, 840, 1; 1, 2880, 1209600, 1209600, 2880, 1; 1, 7560, 10886400, 127008000, 10886400, 7560, 1; 1, 16800, 63504000, 2540160000, 2540160000, 63504000, 16800, 1; 1, 33264, 279417600, 29338848000, 100590336000, 29338848000, 279417600, 33264, 1; MATHEMATICA c[n_]:= c[n]= If[n<3, Fibonacci[n+1], (n-2)!*(n-1)!*n!*(n+1)!*(n+3)!/1440 ]; T[n_, k_]:= c[n]/(c[k]*c[n-k]); Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 16 2021 *) PROG (Magma) F:=Factorial; c:= func< n | n le 2 select Fibonacci(n+1) else F(n-2)*F(n-1)*F(n)*F(n+1)*F(n+3)/1440 >; T:= func< n, k | c(n)/(c(k)*c(n-k)) >; [T(n, k): k in [0..n], n in [0..12]]; // G. C. Greubel, Apr 16 2021 (Sage) f=factorial @CachedFunction def c(n): return fibonacci(n+1) if (n<3) else f(n-2)*f(n-1)*f(n)*f(n+1)*f(n+3)/1440 def T(n, k): return c(n)/(c(k)*c(n-k)) flatten([[T(n, k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Apr 16 2021 CROSSREFS Cf. A173889. Sequence in context: A058293 A172092 A156888 * A159767 A169658 A330199 Adjacent sequences: A173887 A173888 A173889 * A173891 A173892 A173893 KEYWORD nonn,tabl,less,easy AUTHOR Roger L. Bagula, Mar 01 2010 EXTENSIONS Edited by G. C. Greubel, Apr 16 2021 STATUS approved

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Last modified August 6 03:16 EDT 2024. Contains 374957 sequences. (Running on oeis4.)