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 A181738 #35 Sep 14 2018 14:00:43
%S A181738 1,1,1,-2,2,1,-8,-6,3,1,-8,-32,-12,4,1,16,-40,-80,-20,5,1,64,96,-120,
%T A181738 -160,-30,6,1,64,448,336,-280,-280,-42,7,1,-128,512,1792,896,-560,
%U A181738 -448,-56,8,1,-512,-1152,2304,5376,2016,-1008,-672,-72,9,1,-512,-5120,-5760,7680,13440,4032,-1680,-960,-90,10,1
%N A181738 T(n, k) is the coefficient of x^k of the polynomial p(n) which is defined as the scalar part of P(n) = Q(x+1, 1, 1, 1) * P(n-1) for n > 0 and P(0) = Q(1, 0, 0, 0) where Q(a, b, c, d) is a quaternion, triangle read by rows.
%C A181738 The symbol '*' in the name refers to the noncommutative multiplication in Hamilton's division algebra. Traditionally Q(a, b, c, d) is written a + b*i + c*j + d*k.
%H A181738 Peter Luschny, <a href="/A181738/b181738.txt">Rows 0..45, flattened</a>
%H A181738 Wikipedia, <a href="https://en.wikipedia.org/wiki/Quaternion">Quaternion</a>
%e A181738 The list of polynomials starts 1, 1 + x, -2 + 2*x + x^2, -8 - 6*x + 3*x^2 + x^3, ... and the list of coefficients of the polynomials starts:
%e A181738 { 1},
%e A181738 { 1, 1},
%e A181738 { -2, 2, 1},
%e A181738 { -8, -6, 3, 1},
%e A181738 { -8, -32, -12, 4, 1},
%e A181738 { 16, -40, -80, -20, 5, 1},
%e A181738 { 64, 96, -120, -160, -30, 6, 1},
%e A181738 { 64, 448, 336, -280, -280, -42, 7, 1},
%e A181738 {-128, 512, 1792, 896, -560, -448, -56, 8, 1},
%e A181738 {-512, -1152, 2304, 5376, 2016, -1008, -672, -72, 9, 1},
%e A181738 {-512, -5120, -5760, 7680, 13440, 4032, -1680, -960, -90, 10, 1}.
%t A181738 Needs["Quaternions`"]
%t A181738 P[x_, 0 ] := Quaternion[1, 0, 0, 0];
%t A181738 P[x_, n_] := P[x, n] = Quaternion[x + 1, 1, 1, 1] ** P[x, n - 1];
%t A181738 Table[CoefficientList[P[x, n][[1]], x], {n, 0, 10}] // Flatten
%o A181738 (Sage)
%o A181738 R.<x> = QQ[]
%o A181738 K = R.fraction_field()
%o A181738 H.<i,j,k> = QuaternionAlgebra(K, -1, -1)
%o A181738 def Q(a, b, c, d): return H(a + b*i + c*j + d*k)
%o A181738 @cached_function
%o A181738 def P(n):
%o A181738 return Q(x+1,1,1,1)*P(n-1) if n > 0 else Q(1,0,0,0)
%o A181738 def p(n): return P(n)[0].numerator().list()
%o A181738 flatten([p(n) for n in (0..10)]) # Kudos to William Stein, _Peter Luschny_, Sep 14 2018
%Y A181738 Cf. T(n,0) = A138230, A213421 (row sums).
%K A181738 tabl,sign
%O A181738 0,4
%A A181738 _Roger L. Bagula_
%E A181738 Edited by _Peter Luschny_, Sep 14 2018