This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A156933 #13 Apr 14 2021 22:47:01
%S A156933 1,1,1,-11,156,-627,736,591,-1116,-369,-6,106,-2772,76070,-1087552,
%T A156933 8632650,-40358780,106452214,-99774996,-284430514,1125952500,
%U A156933 -1581820542,737716032,414532350,-357790500,-81870750,-1275750
%N A156933 FP4 polynomials related to the o.g.f.s of the columns of the A156925 matrix.
%C A156933 For the matrix of the coefficients of the FP2 see A156925. The coefficients in the columns of this matrix are the powers of z^m, m=0, 1, 2, ... . The columns are numbered: 1, 2, 3, ... .
%C A156933 The GF4(z;m) generate the sequences of the z^m coefficients. The general structure of the GF4(z;m) is given below.
%C A156933 The FP4(z,m) in the numerator of the GF4(z;m) is a polynomial of a certain degree, let's say k4. The (k4+1) coefficients of this polynomial can be determined one by one by comparing the series expansion of the FP4(z,m) with the values of the powers of z^m in column (m+1). These values can be generated with the GF2 formulas, see A156925.
%C A156933 An appropriate name for the polynomials FP4(z;m) in the numerators of the GF4(z;m) seems to be the flower polynomials of the fourth kind because the zero patterns of these polynomials look like flowers. The zero patterns of the FP4 and the FP3, see A156927, resemble each other closely and look like the zero patterns of the FP1 and FP2.
%C A156933 The sequence of (k4+1) number of terms of the FP4(z;m) polynomials for m from 0 to 11 is 1, 2, 7, 17, 28, 44, 63, 83, 108, 136, 167, 199.
%F A156933 G.f.: GF4(z;m):= z^q*FP4(z;m) / Product_{k=0..m} (1-(2*m+1-(2*k))*z)^(3*k+1).
%e A156933 The first few rows of the "triangle" of the FP4(z;m) coefficients are:
%e A156933 [1]
%e A156933 [1, 1]
%e A156933 [ -11, 156, -627, 736, 591, -1116, -369]
%e A156933 The first few FP4 polynomials are:
%e A156933 FP4(z; m=0) = 1
%e A156933 FP4(z; m=1) = (1+z)
%e A156933 FP4(z; m=2) = ( -11+156*z-627*z^2+736*z^3+591*z^4-1116*z^5-369*z^6 )
%e A156933 Some GF4(z;m) are:
%e A156933 GF4(z;m=1) = z*(1+z)/((1-3*z)*(1-z)^4)
%e A156933 GF4(z;m=2) = z^2*(-11+156*z-627*z^2+736*z^3+591*z^4-1116*z^5-369*z^6)/((1-z)^7*(1-3*z)^4*(1-5*z))
%Y A156933 Cf. A156920, A156921, A156925, A156927.
%Y A156933 For the first few GF4's see A156934, A156935, A156936, A156937.
%Y A156933 Row sums A156938.
%Y A156933 For the polynomials in the denominators of the GF4(z;m) see A157705. - _Johannes W. Meijer_, Mar 07 2009
%K A156933 easy,sign,tabf,uned
%O A156933 0,4
%A A156933 _Johannes W. Meijer_, Feb 20 2009