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 A100257 Triangle of expansions of 2^(k-1)*x^k in terms of T(n,x), in descending degrees n of T, with T the Chebyshev polynomials. 18
 1, 1, 0, 1, 0, 1, 1, 0, 3, 0, 1, 0, 4, 0, 3, 1, 0, 5, 0, 10, 0, 1, 0, 6, 0, 15, 0, 10, 1, 0, 7, 0, 21, 0, 35, 0, 1, 0, 8, 0, 28, 0, 56, 0, 35, 1, 0, 9, 0, 36, 0, 84, 0, 126, 0, 1, 0, 10, 0, 45, 0, 120, 0, 210, 0, 126, 1, 0, 11, 0, 55, 0, 165, 0, 330, 0, 462, 0, 1, 0, 12, 0, 66, 0, 220, 0 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 REFERENCES M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 795. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..6104 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. H. J. Brothers, Pascal's Prism: Supplementary Material. EXAMPLE x^0 = T(0,x) x^1 = T(1,x) + 0T(0,x) 2x^2 = T(2,x) + 0T(1,x) + 1T(0,x) 4x^3 = T(3,x) + 0T(2,x) + 3T(1,x) + 0T(0,x) 8x^4 = T(4,x) + 0T(3,x) + 4T(2,x) + 0T(1,x) + 3T(0,x) 16x^5 = T(5,x) + 0T(4,x) + 5T(3,x) + 0T(2,x) + 10T(1,x) + 0T(0,x) MATHEMATICA a[k_, n_] := If[k == 1, 1, If[EvenQ[n] || k < 0 || n > k, 0, If[n >= k - 1, Binomial[2*Floor[k/2], Floor[k/2]]/2, Binomial[k - 1, Floor[n/2]]]]]; Table[a[k, n], {k, 1, 13}, {n, 1, k}] // Flatten (* Jean-François Alcover, May 04 2017, translated from PARI *) PROG (PARI) a(k, n)=if(k==1, 1, if(n%2==0||k<0||n>k, 0, if(n>=k-1, binomial(2*floor(k/2), floor(k/2))/2, binomial(k-1, floor(n/2))))) CROSSREFS Without zeros: A008311. Row sums are A011782. Cf. A092392. Diagonals are (with interleaved zeros) twice A001700, A001791, A002054, A002694, A003516, A002696, A030053, A004310, A030054, A004311, A030055, A004312, A030056, A004313. Sequence in context: A117178 A111527 A035695 * A318315 A300228 A100573 Adjacent sequences:  A100254 A100255 A100256 * A100258 A100259 A100260 KEYWORD nonn,tabl AUTHOR Ralf Stephan, Nov 13 2004 STATUS approved

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Last modified October 13 18:57 EDT 2019. Contains 327981 sequences. (Running on oeis4.)