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%I #26 Dec 26 2017 01:23:11
%S 1,11,1,110,12,1,1100,122,13,1,11000,1222,135,14,1,110000,12222,1357,
%T 149,15,1,1100000,122222,13579,1506,164,16,1,11000000,1222222,135801,
%U 15085,1670,180,17,1
%N Generalized Lucas-Pascal triangle; (11*10^n, 1).
%H Robert Israel, <a href="/A164851/b164851.txt">Table of n, a(n) for n = 0..10010</a>(rows 0 to 140, flattened)
%F T(0,0)=1, T(n+1,0)=11*10^n, T(n,n)=1, T(n,k)=T(n-1,k-1)+T(n-1,k) for 0<k<n. - _Philippe Deléham_, Dec 27 2013
%F G.f. as triangle: (1-x^2)/((1-10*x)*(1-x-x*y)). - _Robert Israel_, Jul 17 2017
%e Triangle begins:
%e 1;
%e 11, 1;
%e 110, 12, 1;
%e 1100, 122, 13, 1;
%e 11000, 1222, 135, 14, 1;
%e 110000, 12222, 1357, 149, 15, 1;
%e 1100000, 122222, 13579, 1506, 164, 16, 1;
%e 11000000,1222222, 135801, 15085, 1670, 180, 17, 1;
%e ...
%p G[0]:= 1;
%p G[1]:= 11+x;
%p G[2]:= 110+12*x+x^2;
%p for nn from 3 to 20 do
%p G[nn]:= expand((x+11)*G[nn-1]-10*(x+1)*G[nn-2]);
%p od:
%p seq(seq(coeff(G[n],x,j),j=0..n),n=0..20); # _Robert Israel_, Jul 17 2017
%t T[0, 0] := 1; T[n_, n_] := 1; T[n_, 0] := 11*10^(n - 1); T[n_, k_] := T[n - 1, k - 1] + T[n - 1, k]; Table[T[n, k], {n, 0, 10}, {k, 0, n}] //Flatten (* _G. C. Greubel_, Dec 22 2017 *)
%Y Cf. A029635, A164844, A228196.
%K nonn,tabl
%O 0,2
%A _Mark Dols_, Aug 28 2009
%E Initial 1 added by _Philippe Deléham_, Dec 27 2013