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 A157243 Triangle T(n, k) = A001263(n*f(n,k) + 1, f(n,k) + 1), where f(n, k) = k if k <= floor(n/2) otherwise n-k, read by rows. 1
 1, 1, 1, 1, 3, 1, 1, 6, 6, 1, 1, 10, 336, 10, 1, 1, 15, 825, 825, 15, 1, 1, 21, 1716, 197676, 1716, 21, 1, 1, 28, 3185, 512050, 512050, 3185, 28, 1, 1, 36, 5440, 1163800, 294296640, 1163800, 5440, 36, 1, 1, 45, 8721, 2395575, 778076145, 778076145, 2395575, 8721, 45, 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) = A001263(n*f(n,k) + 1, f(n,k) + 1), where f(n, k) = k if k <= floor(n/2) otherwise n-k. T(n, n-k) = T(n, k)). T(n, 1) = A000217(n). - G. C. Greubel, Jan 11 2022 EXAMPLE Triangle begins as: 1; 1, 1; 1, 3, 1; 1, 6, 6, 1; 1, 10, 336, 10, 1; 1, 15, 825, 825, 15, 1; 1, 21, 1716, 197676, 1716, 21, 1; 1, 28, 3185, 512050, 512050, 3185, 28, 1; 1, 36, 5440, 1163800, 294296640, 1163800, 5440, 36, 1; 1, 45, 8721, 2395575, 778076145, 778076145, 2395575, 8721, 45, 1; MATHEMATICA f[n_, k_]:= If[k<=Floor[n/2], k, n-k]; A001263[n_, k_]:= Binomial[n-1, k-1]*Binomial[n, k]/(n-k+1); T[n_, k_]:= A001263[n*f[n, k] +1, f[n, k] +1]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Jan 11 2022 *) PROG (Magma) f:= func< n, k | k le Floor(n/2) select k else n-k >; A001263:= func< n, k | Binomial(n-1, k-1)*Binomial(n, k)/(n-k+1) >; [A001263(n*f(n, k)+1, f(n, k)+1): k in [0..n], n in [0..12]]; // G. C. Greubel, Jan 11 2022 (Sage) def f(n, k): return k if (k <= (n//2)) else n-k def A001263(n, k): return binomial(n-1, k-1)*binomial(n, k)/(n-k+1) flatten([[A001263(n*f(n, k)+1, f(n, k)+1) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Jan 11 2022 CROSSREFS Cf. A000217, A001263, A157219, A157221. Sequence in context: A180959 A131235 A202812 * A146769 A189610 A172427 Adjacent sequences: A157240 A157241 A157242 * A157244 A157245 A157246 KEYWORD nonn,tabl AUTHOR Roger L. Bagula, Feb 25 2009 EXTENSIONS Edited by G. C. Greubel, Jan 11 2022 STATUS approved

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Last modified September 8 22:43 EDT 2024. Contains 375759 sequences. (Running on oeis4.)