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 A207824 Triangle of coefficients of Chebyshev's S(n,x+5) polynomials (exponents of x in increasing order). 7
 1, 5, 1, 24, 10, 1, 115, 73, 15, 1, 551, 470, 147, 20, 1, 2640, 2828, 1190, 246, 25, 1, 12649, 16310, 8631, 2400, 370, 30, 1, 60605, 91371, 58275, 20385, 4225, 519, 35, 1, 290376, 501150, 374115, 157800, 41140, 6790, 693, 40, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Riordan array (1/(1-5*x+x^2), x/(1-5*x+x^2)). Subtriangle of triangle given by (0, 5, -1/5, 1/5, 0, 0, 0, 0, 0, 0, 0, 0...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. Unsigned version of A123967 and A179900. For 1<=k<=n, T(n,k) equals the number of (n-1)-length words over {0,1,2,3,4,5} containing k-1 letters equal 5 and avoiding 01. - Milan Janjic, Dec 20 2016 LINKS Michael De Vlieger, Table of n, a(n) for n = 0..11475 (rows 0 <= n <= 150) Milan Janjić, Words and Linear Recurrences, J. Int. Seq. 21 (2018), #18.1.4. FORMULA Recurrence : T(n,k) = 5*T(n-1,k) + T(n-1,k-1) - T(n-2,k). G.f.: 1/(1-5*x+x^2-y*x). Diagonal sums are 5^n = A000351(n). Row sums are A001109(n+1). T(n,0) = A004254(n+1), T(n+1,n) = 5n+5 = A008587(n+1). EXAMPLE Triangle begins : 1 5, 1 24, 10, 1 115, 73, 15, 1 551, 470, 147, 20, 1 2640, 2828, 1190, 246, 25, 1 12649, 16310, 8631, 2400, 370, 30, 1 ... Triangle (0, 5, -1/5, 1/5, 0, 0, 0,...) DELTA (1, 0, 0, 0, ...) begins : 1 0, 1 0, 5, 1 0, 24, 10, 1 0, 115, 73, 15, 1 0, 551, 470, 147, 20, 1 0, 2640, 2828, 1190, 246, 25, 1 ... MATHEMATICA With[{n = 8}, DeleteCases[#, 0] & /@ CoefficientList[Series[1/(1 - 5 x + x^2 - y x), {x, 0, n}, {y, 0, n}], {x, y}]] // Flatten (* Michael De Vlieger, Apr 25 2018 *) PROG (PARI) row(n) = Vecrev(polchebyshev(n, 2, (x+5)/2)); \\ Michel Marcus, Apr 26 2018 CROSSREFS Cf. Triangles of coefficients of Chebyshev's S(n,x+k) polynomials : A207824 (k = 5), A207823 (k = 4), A125662 (k = 3), A078812 (k = 2), A101950 (k = 1), A049310 (k = 0), A104562 (k = -1), A053122 (k = -2), A207815 (k = -3), A159764 (k = -4), A123967 (k = -5). Sequence in context: A146675 A201884 A294138 * A179900 A123967 A162259 Adjacent sequences: A207821 A207822 A207823 * A207825 A207826 A207827 KEYWORD easy,nonn,tabl AUTHOR Philippe Deléham, Feb 20 2012 STATUS approved

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Last modified March 28 14:02 EDT 2023. Contains 361595 sequences. (Running on oeis4.)