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A257598 Triangle read by rows: coefficients of polynomials W_n(x), highest degree terms first.

%I A257598 #20 Aug 22 2015 03:00:52
%S A257598 1,1,1,2,1,1,4,1,1,1,8,1,1,1,16,-4,1,1,1,1,32,-16,2,1,1,1,1,64,-48,8,
%T A257598 1,1,1,1,1,128,-128,32,1,1,1,1,1,256,-320,112,-8,1,1,1,1,1,1,512,-768,
%U A257598 352,-48,2,1,1,1,1,1,1
%N A257598 Triangle read by rows: coefficients of polynomials W_n(x), highest degree terms first.
%H A257598 K. Dilcher, K. B. Stolarsky, <a href="http://dx.doi.org/10.1007/s11139-014-9620-5">Nonlinear recurrences related to Chebyshev polynomials</a>, The Ramanujan Journal, 2014, Online Oct. 2014, pp. 1-23.
%F A257598 W(n) = V(n+1)^2 - V(n)*V(n+2) where V(n) are the polynomials defined in A257597. - _Michel Marcus_, Aug 22 2015
%e A257598 Triangle of coefficients begins:
%e A257598 1,
%e A257598 1, 1,
%e A257598 2, 1, 1,
%e A257598 4, 1, 1, 1,
%e A257598 8, 1, 1, 1,
%e A257598 16, -4, 1, 1, 1, 1,
%e A257598 32, -16, 2, 1, 1, 1, 1,
%e A257598 64, -48, 8, 1, 1, 1, 1, 1,
%e A257598 128, -128, 32, 1, 1, 1, 1, 1,
%e A257598 256, -320, 112 -8, 1, 1, 1, 1, 1, 1,
%e A257598 512, -768, 352 -48, 2, 1, 1, 1, 1, 1, 1,
%e A257598 ...
%e A257598 The actual polynomials are:
%e A257598 0 1
%e A257598 1 x^2 + 1
%e A257598 2 2x^4 + x^2 + 1
%e A257598 3 4x^6 + x^4 + x^2 + 1
%e A257598 4 8x^8 + x^4 + x^2 + 1
%e A257598 5 16x^10 - 4x^8 + x^6 + x^4 + x^2 + 1
%e A257598 6 32x^12 - 16x^10 + 2x^8 + x^6 + x^4 + x^2 + 1
%e A257598 7 64x^14 - 48x^12 + 8x^10 + x^8 + x^6 + x^4 + x^2 + 1
%e A257598 8 128x^16 - 128x^14 + 32x^12 + x^8 + x^6 + x^4 + x^2 + 1
%e A257598 9 256x^18 - 320x^16 + 112x^14 - 8x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1
%e A257598 10 512x^20 - 768x^18 + 352x^16 - 48x^14 + 2x^12 + x^10 + x^8 + x^6 + x^4 + x^2 + 1
%e A257598 ...
%o A257598 (PARI) tabf(nn) = {pp = 1; p = x; for (n=1, nn, np = 2*x*p-pp-x^(n+1); w = p^2 - pp*np; forstep (j=poldegree(w), 0, -1, if (c = polcoeff(w, j), print1(c, ", "));); pp = p; p = np; print(););} \\ _Michel Marcus_, Aug 22 2015
%Y A257598 Cf. A257597.
%K A257598 sign,tabl
%O A257598 0,4
%A A257598 _N. J. A. Sloane_, Jun 06 2015
%E A257598 One typo in data corrected by _Michel Marcus_, Aug 22 2015