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 A104878 #31 May 04 2021 21:14:36 %S A104878 1,1,1,1,2,1,1,3,3,1,1,4,7,4,1,1,5,15,13,5,1,1,6,31,40,21,6,1,1,7,63, %T A104878 121,85,31,7,1,1,8,127,364,341,156,43,8,1,1,9,255,1093,1365,781,259, %U A104878 57,9,1,1,10,511,3280,5461,3906,1555,400,73,10,1,1,11,1023,9841,21845 %N A104878 A sum-of-powers number triangle. %C A104878 Columns are partial sums of the columns of A004248. Row sums are A104879. Diagonal sums are A104880. %C A104878 The rows of this triangle (apart from the initial "1" in each row) are the antidiagonals of rectangle A055129. The diagonals of this triangle (apart from the initial "1") are the rows of rectangle A055129. The columns of this triangle (apart from the leftmost column) are the same as the columns of rectangle A055129 but shifted downward. - _Mathew Englander_, Dec 21 2020 %F A104878 T(n, k) = if(k=1, n, if(k<=n, (k^(n-k+1)-1)/(k-1), 0)); %F A104878 G.f. of column k: x^k/((1-x)(1-k*x)). [corrected by _Werner Schulte_, Jun 05 2019] %F A104878 T(n, k) = A069777(n+1,k)/A069777(n,k). [_Johannes W. Meijer_, Aug 21 2011] %F A104878 T(n, k) = A055129(n+1-k, k) for n >= k > 0. - _Mathew Englander_, Dec 19 2020 %e A104878 Triangle starts: %e A104878 1; %e A104878 1, 1; %e A104878 1, 2, 1; %e A104878 1, 3, 3, 1; %e A104878 1, 4, 7, 4, 1; %e A104878 1, 5, 15, 13, 5, 1; %e A104878 1, 6, 31, 40, 21, 6, 1; %e A104878 ... %p A104878 A104878 :=proc(n,k): if k = 0 then 1 elif k=1 then n elif k>=2 then (k^(n-k+1)-1)/(k-1) fi: end: for n from 0 to 7 do seq(A104878(n,k), k=0..n) od; seq(seq(A104878(n,k), k=0..n), n=0..10); # _Johannes W. Meijer_, Aug 21 2011 %Y A104878 Cf. A004248 (first differences by column), A104879 (row sums), A104880 (antidiagonal sums), A125118 (version of this triangle with fewer terms). %Y A104878 This triangle (ignoring the leftmost column) is a rotation of rectangle A055129. %Y A104878 Columns (adjusting offset as necessary): A000012, A000027, A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724, A218725, A218726, A218727, A218728, A218729, A218730, A218731, A218732, A218733, A218734, A132469, A218736, A218737, A218738, A218739, A218740, A218741, A218742, A218743, A218744, A218745, A218746, A218747, A218748, A218749, A218750, A218751, A218753, A218752. %Y A104878 T(2n,n) gives A031973. %K A104878 easy,nonn,tabl %O A104878 0,5 %A A104878 _Paul Barry_, Mar 28 2005