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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 May 5 17:26 EDT 2021. Contains 343572 sequences. (Running on oeis4.)