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 A172497 Triangle T(n, k) = round( c(n)/(c(k)*c(n-k)) ) where c(n) = Product_{j=1..n} A029826(j+10), read by rows. 1
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 2, 4, 2, 2, 1, 1, 3, 6, 6, 6, 6, 3, 1, 1, 2, 6, 12, 6, 12, 6, 2, 1, 1, 4, 8, 24, 24, 24, 24, 8, 4, 1, 1, 3, 12, 24, 36, 72, 36, 24, 12, 3, 1, 1, 5, 15, 60, 60, 180, 180, 60, 60, 15, 5, 1, 1, 5, 25, 75, 150, 300, 450, 300, 150, 75, 25, 5, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,12 LINKS G. C. Greubel, Rows n = 0..50 of the triangle, flattened FORMULA T(n, k) = round( c(n)/(c(k)*c(n-k)) ) where c(n) = Product_{j=1..n} A029826(j+10). EXAMPLE The triangle begins as: 1; 1, 1; 1, 1, 1; 1, 1, 1, 1; 1, 2, 2, 2, 1; 1, 1, 2, 2, 1, 1; 1, 2, 2, 4, 2, 2, 1; 1, 3, 6, 6, 6, 6, 3, 1; 1, 2, 6, 12, 6, 12, 6, 2, 1; 1, 4, 8, 24, 24, 24, 24, 8, 4, 1; 1, 3, 12, 24, 36, 72, 36, 24, 12, 3, 1; MATHEMATICA b:= Drop[CoefficientList[Series[1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10), {x, 0, 100}], x], 10]; c[n_]:= Product[b[[j]], {j, n}]; T[n_, k_]:= Round[c[n]/(c[k]*c[n-k])]; Table[T[n, k], {n, 0, 12}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Apr 20 2021 *) PROG (Magma) R:= PowerSeriesRing(Integers(), 100); b:= Coefficients(R!( 1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10) )); c:= func< n | (&*[b[j]: j in [10..n+10]]) >; T:= func< n, k | Round(c(n)/(c(k)*c(n-k))) >; [T(n, k): k in [0..n], n in [1..12]]; // G. C. Greubel, Apr 20 2021 (Sage) @CachedFunction def A029826_list(prec): P. = PowerSeriesRing(ZZ, prec) return P( 1/(1+x-x^3-x^4-x^5-x^6-x^7+x^9+x^10) ).list() b=A029826_list(130) def c(n): return product(b[j] for j in (9..n+9)) def T(n, k): return round(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 20 2021 CROSSREFS Cf. A029826. Sequence in context: A238408 A048858 A246465 * A211226 A306366 A135265 Adjacent sequences: A172494 A172495 A172496 * A172498 A172499 A172500 KEYWORD nonn,tabl,easy,less AUTHOR Roger L. Bagula, Feb 05 2010 EXTENSIONS Definition corrected and edited by G. C. Greubel, Apr 20 2021 STATUS approved

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Last modified July 20 05:10 EDT 2024. Contains 374441 sequences. (Running on oeis4.)