Mfcttrf

How can I make number pattern like this

But, every spaces is replaced with plus sign ?

Just for fun: without packages.

documentclassarticle
newcounterpft
newcounterpfft
begindocument
setcounterpft0loop%
stepcounterpft%
setcounterpfft0noindent$loop%
stepcounterpfftnumbervaluepfft%
ifnumnumbervaluepfft<numbervaluepft+repeat$par%
ifnumnumbervaluepft<11repeat%
enddocument

Or with pgffor, which contains the foreach command that is used in JouleV's nice answer, and which is loaded by TikZ.

documentclassarticle
usepackagepgffor
begindocument
foreach X in 1,...,11%
noindent$foreach Y in 1,...,X%
ifnumY>1%
+%
fi%
Y
$par
enddocument

Let's employ TikZ and some simple algorithms for such things.

documentclass[tikz]standalone
begindocument
begintikzpicture[x=5ex,y=5ex]
foreach i in 1,...,11 
 % Draw the numbers
 pgfmathsetmacroresult12-i
 foreach j in 1,...,result 
 node (i-j) at (i,j) i;
 % Draw the plus signs
 ifnumi=11relaxelse
 pgfmathsetmacroresult11-i
 foreach j in 1,...,result 
 node[anchor=base] at ([shift=(.5,0)]i-j.base) +;
 fi

endtikzpicture
enddocument

A little bonus:

documentclass[tikz]standalone
begindocument
begintikzpicture[x=5ex,y=5ex]
foreach i in 1,...,11 
 % numbers
 pgfmathsetmacroresult12-i
 foreach j in 1,...,result 
 node (i-j) at (i,j) i;
 % plus signs
 ifnumi=11relaxelse
 pgfmathsetmacroresult11-i
 foreach j in 1,...,result 
 node[anchor=base] at ([shift=(.5,0)]i-j.base) +;
 fi
 % the rest :)
 pgfmathsetmacrosumoutputint((12-i)*(13-i)/2)
 node (output-i) at (12,i) sumoutput;
 node[anchor=base] at ([shift=(-.5,0)]output-i.base) =;

endtikzpicture
enddocument

Not sure what do you really want to get by "to the right", but maybe this?

documentclass[tikz]standalone
begindocument
begintikzpicture[x=5ex,y=5ex]
foreach i in 1,...,11 
 % numbers - simpler than the above code
 foreach j [count=k] in i,...,1
 node (i-j) at (i,j) k;
 % plus signs - a bit simpler
 ifnumi=11relaxelse
 foreach j in i,...,1 
 node[anchor=base] at ([shift=(.5,0)]i-j.base) +;
 fi
 % I keep the "bonus" part - it needs no improvements
 pgfmathsetmacrosumoutputint((12-i)*(13-i)/2)
 node (output-i) at (12,i) sumoutput;
 node[anchor=base] at ([shift=(-.5,0)]output-i.base) =;

endtikzpicture
enddocument

A LuaLaTeX-based solution:

To make the triangular array right-aligned instead of left-aligned, change @l@ to @r@. If you wish to have a bit more space around the + symbols, change + to +.

documentclassarticle
usepackageluacode

beginluacode

function make_array(n)
 tex.sprint ( "\beginarray@l@" )
 for i=1,n do
 for j=1,i do
 tex.sprint ( j )
 if j<i then 
 tex.sprint ("+")
 else
 tex.sprint ("\\")
 end
 end
 end
 tex.sprint ( "\endarray" )
end

endluacode
newcommandmakearray[1]directluamake_array(#1)

begindocument
$makearray11$
enddocument

documentclassarticle
usepackagemultido
begindocument
noindent$1$
multidoiA=2+110\$%
 multidoiB=1+1numexpriA-1iB+iA$

bigskipnoindent$1=1$
multidoiA=2+110\$xdefSum0%
 multidoiB=1+1numexpriA-1%
 iB+xdefSumthenumexprSum+iBiA=thenumexprSum+iA$

enddocument