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 A159764 Riordan array (1/(1+4x+x^2), x/(1+4x+x^2)). 13
 1, -4, 1, 15, -8, 1, -56, 46, -12, 1, 209, -232, 93, -16, 1, -780, 1091, -592, 156, -20, 1, 2911, -4912, 3366, -1200, 235, -24, 1, -10864, 21468, -17784, 8010, -2120, 330, -28, 1, 40545, -91824, 89238, -48624, 16255, -3416, 441, -32, 1, -151316, 386373 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Row sums are (-1)^n*F(2n+2). Diagonal sums are (-1)^n*4^n. Inverse is A052179. The positive matrix is (1/(1-4x+x^2), x/(1-4x+x^2)) with general term T(n,k) = if(k<=n, Gegenbauer_C(n-k,k+1,2),0). For another version, see A124029. Triangle of coefficients of Chebyshev's S(n,x-4) polynomials (exponents of x in increasing order). - Philippe Deléham, Feb 22 2012 Subtriangle of triangle given by (0, -4, 1/4, -1/4, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Feb 22 2012 LINKS G. C. Greubel, Rows n=0..100 of triangle, flattened FORMULA Number triangle T(n,k) = if(k<=n, Gegenbauer_C(n-k,k+1,-2),0). G.f.: 1/(1+4*x+x^2-y*x). - Philippe Deléham, Feb 22 2012 T(n,k) = (-4)*T(n-1,k) + T(n-1,k-1) - T(n-2,k). - Philippe Deléham, Feb 22 2012 EXAMPLE Triangle begins      1;     -4,     1;     15,    -8,     1;    -56,    46,   -12,     1;    209,  -232,    93,   -16,     1;   -780,  1091,  -592,   156,   -20,     1;   2911, -4912,  3366, -1200,   235,   -24,     1; Triangle (0, -4, 1/4, -1/4, 0, 0, 0, ...) DELTA (1, 0, 0, 0, ...) begins:   1;   0,    1;   0,   -4,    1;   0,   15,   -8,    1;   0,  -56,   46,  -12,    1;   0,  209, -232,   93,  -16,    1; MATHEMATICA CoefficientList[CoefficientList[Series[1/(1 + 4*x + x^2 - y*x), {x, 0, 10}, {y, 0, 10}], x], y]//Flatten (* G. C. Greubel, May 21 2018 *) PROG (Sage) @CachedFunction def A159764(n, k):     if n< 0: return 0     if n==0: return 1 if k == 0 else 0     return A159764(n-1, k-1)-A159764(n-2, k)-4*A159764(n-1, k) for n in (0..9): [A159764(n, k) for k in (0..n)] # Peter Luschny, Nov 20 2012 CROSSREFS Cf. Triangle of coefficients of Chebyshev's S(n,x+k) polynomials : A207824, A207823, A125662, A078812, A101950, A049310, A104562, A053122, A207815, A159764, A123967 for k = 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5 respectively. Sequence in context: A156290 A080419 A095307 * A124029 A207823 A056920 Adjacent sequences:  A159761 A159762 A159763 * A159765 A159766 A159767 KEYWORD easy,sign,tabl AUTHOR Paul Barry, Apr 21 2009 STATUS approved

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Last modified December 1 14:10 EST 2021. Contains 349430 sequences. (Running on oeis4.)