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A164851 Generalized Lucas-Pascal triangle; (11*10^n, 1).

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