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 A022174 #42 May 09 2025 10:34:30
%S A022174 1,1,1,1,11,1,1,111,111,1,1,1111,11211,1111,1,1,11111,1122211,1122211,
%T A022174 11111,1,1,111111,112232211,1123333211,112232211,111111,1,1,1111111,
%U A022174 11223332211,1123445443211,1123445443211,11223332211,1111111,1
%N A022174 Triangle of Gaussian binomial coefficients [ n,k ] for q = 10.
%D A022174 F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, Elsevier-North Holland, 1978, p. 698.
%H A022174 G. C. Greubel, <a href="/A022174/b022174.txt">Rows n=0..50 of triangle, flattened</a>
%H A022174 Kent E. Morrison, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL9/Morrison/morrison37.html">Integer Sequences and Matrices Over Finite Fields</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
%H A022174 <a href="/index/Ga#Gaussian_binomial_coefficients">Index entries for sequences related to Gaussian binomial coefficients</a>
%F A022174 T(n,k) = T(n-1,k-1) + q^k * T(n-1,k). - _Peter A. Lawrence_, Jul 13 2017
%F A022174 G.f. of column k: x^k * exp( Sum_{j>=1} f((k+1)*j)/f(j) * x^j/j ), where f(j) = 10^j - 1. - _Seiichi Manyama_, May 09 2025
%e A022174 Triangle begins:
%e A022174 1;
%e A022174 1, 1;
%e A022174 1, 11, 1;
%e A022174 1, 111, 111, 1;
%e A022174 1, 1111, 11211, 1111, 1;
%e A022174 1, 11111, 1122211, 1122211, 11111, 1;
%e A022174 1, 111111, 112232211, 1123333211, 112232211, 111111, 1;
%e A022174 1, 1111111, 11223332211, 1123445443211, 1123445443211, 11223332211, 1111111, 1;
%p A022174 A027878 := proc(n)
%p A022174 mul(10^i-1,i=1..n) ;
%p A022174 end proc:
%p A022174 A022174 := proc(n,m)
%p A022174 A027878(n)/A027878(m)/A027878(n-m) ;
%p A022174 end proc:# _R. J. Mathar_, Jul 19 2017
%t A022174 a027878[n_]:=Times@@ Table[10^i - 1, {i, n}]; T[n_, m_]:=a027878[n]/( a027878[m] a027878[n - m]); Table[T[n, m], {n, 0, 10}, {m, 0, n}]//Flatten (* _Indranil Ghosh_, Jul 20 2017, after Maple code *)
%t A022174 Table[QBinomial[n,k,10], {n,0,10}, {k,0,n}]//Flatten (* or *) q:= 10; T[n_, 0]:= 1; T[n_,n_]:= 1; T[n_,k_]:= T[n,k] = If[k < 0 || n < k, 0, T[n-1, k -1] +q^k*T[n-1,k]]; Table[T[n,k], {n,0,10}, {k,0,n}] // Flatten (* _G. C. Greubel_, May 28 2018 *)
%o A022174 (Python)
%o A022174 from operator import mul
%o A022174 def a027878(n): return 1 if n==0 else reduce(mul, [10**i - 1 for i in range(1, n + 1)])
%o A022174 def T(n, m): return a027878(n)/(a027878(m)*a027878(n - m))
%o A022174 for n in range(11): print([T(n, m) for m in range(n + 1)]) # _Indranil Ghosh_, Jul 20 2017, after Maple code
%o A022174 (PARI) {q=10; T(n,k) = if(k==0,1, if (k==n, 1, if (k<0 || n<k, 0, T(n-1,k-1) + q^k*T(n-1,k))))};
%o A022174 for(n=0,10, for(k=0,n, print1(T(n,k), ", "))) \\ _G. C. Greubel_, May 28 2018
%Y A022174 Row sums give A015196.
%K A022174 nonn,tabl
%O A022174 0,5
%A A022174 _N. J. A. Sloane_