%I A125118
%S A125118 1,3,4,7,13,21,15,40,85,156,31,121,341,781,1555,63,364,1365,3906,9331,
%T A125118 19608,127,1093,5461,19531,55987,137257,299593,255,3280,21845,97656,
%U A125118 335923,960800,2396745,5380840,511,9841,87381,488281,2015539,6725601
%N A125118 Triangle read by rows: T(n,k) = value of the n-th repunit in base (k+1) 
               representation, 1<=k<=n.
%C A125118 T(n+1,k) = (k+1)*T(n,k) + 1;
%C A125118 row sums give A125120; central terms give A125119;
%C A125118 T(n,1) = A000225(n);
%C A125118 T(n,2) = A003462(n) for n>1;
%C A125118 T(n,3) = A002450(n) for n>2;
%C A125118 T(n,4) = A003463(n) for n>3;
%C A125118 T(n,5) = A003464(n) for n>4;
%C A125118 T(n,9) = A002275(n) for n>8;
%C A125118 T(n,n-2) = A031973(n) for n>2;
%C A125118 T(n,n-1) = A023037(n) for n>1;
%C A125118 T(n,n) = A060072(n+1);
%H A125118 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Repunit.html">Repunit</a>
%F A125118 T(n,k) = Sum((k+1)^i: 0<=i<n).
%e A125118 First 4 rows:
%e A125118 1: [1]_2
%e A125118 2: [11]_2 ........ [11]_3
%e A125118 3: [111]_2 ....... [111]_3 ....... [111]_4
%e A125118 4: [1111]_2 ...... [1111]_3 ...... [1111]_4 ...... [1111]_5
%e A125118 _
%e A125118 1: 1
%e A125118 2: 2+1 ........... 3+1
%e A125118 3: (2+1)*2+1 ..... (3+1)*3+1 ..... (4+1)*4+1
%e A125118 4: ((2+1)*2+1)*2+1 ((3+1)*3+1)*3+1 ((4+1)*4+1)*4+1
%e A125118 ((5+1)*5+1)*5+1.
%Y A125118 Sequence in context: A055664 A089374 A029552 this_sequence A116201 A092406 
               A121174
%Y A125118 Adjacent sequences: A125115 A125116 A125117 this_sequence A125119 A125120 
               A125121
%K A125118 nonn,tabl,base
%O A125118 1,2
%A A125118 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 21 2006