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A135936 Irregular triangle read by rows: row n gives coefficients of Boubaker polynomial B_n(x) in order of decreasing exponents (another version). 4

%I

%S 1,1,1,2,1,1,1,0,-2,1,-1,-3,1,-2,-3,2,1,-3,-2,5,1,-4,0,8,-2,1,-5,3,10,

%T -7,1,-6,7,10,-15,2,1,-7,12,7,-25,9,1,-8,18,0,-35,24,-2,1,-9,25,-12,

%U -42,49,-11,1,-10,33,-30,-42,84,-35,2,1,-11,42,-55,-30,126,-84,13,1,-12,52,-88,0,168,-168,48,-2,1,-13,63,-130,55,198,-294

%N Irregular triangle read by rows: row n gives coefficients of Boubaker polynomial B_n(x) in order of decreasing exponents (another version).

%C See A135929 and A138034 for further information.

%H R. J. Mathar, Mar 11 2008, <a href="/A135936/b135936.txt">Table of n, a(n) for n = 0..160</a>

%F Conjectures from _Thomas Baruchel_, Jun 03 2018: (Start)

%F T(n,m) = 4*A115139(n+1,m) - 3*A132460(n,m).

%F T(n,m) = (-1)^m * (binomial(n-m, m) - 3*binomial(n-m-1, m-1)). (End)

%e The Boubaker polynomials B_0(x), B_1(x), B_2(x), ... are:

%e 1

%e x

%e x^2 + 2

%e x^3 + x

%e x^4 - 2

%e x^5 - x^3 - 3*x

%e x^6 - 2*x^4 - 3*x^2 + 2

%e x^7 - 3*x^5 - 2*x^3 + 5*x

%e x^8 - 4*x^6 + 8*x^2 - 2

%e x^9 - 5*x^7 + 3*x^5 + 10*x^3 - 7*x

%e ...

%p A135936 := proc(n,m) coeftayl( coeftayl( (1+3*t^2)/(1-x*t+t^2),t=0,n), x=0,m) ; end: for n from 0 to 25 do for m from n to 0 by -2 do printf("%d, ",A135936(n,m)) ; od; od; # _R. J. Mathar_, Mar 11 2008

%Y Cf. A138034.

%K sign,tabf

%O 0,4

%A _N. J. A. Sloane_, Mar 09 2008

%E More terms from _R. J. Mathar_, Mar 11 2008

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Last modified October 21 16:20 EDT 2019. Contains 328302 sequences. (Running on oeis4.)