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A104878 A sum-of-powers number triangle. 5

%I

%S 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 121,85,31,7,1,1,8,127,364,341,156,43,8,1,1,9,255,1093,1365,781,259,

%U 57,9,1,1,10,511,3280,5461,3906,1555,400,73,10,1,1,11,1023,9841,21845

%N A sum-of-powers number triangle.

%C Columns are partial sums of the columns of A004248. Row sums are A104879. Diagonal sums are A104880.

%F Number triangle T(n, k) = if(k=1, n, if(k<=n, (k^(n-k+1)-1)/(k-1), 0));

%F Number triangle whose columns have g.f. 1/((1-x)(1-x)^k).

%F T(n,k) = A069777(n+1,k)/A069777(n,k). [_Johannes W. Meijer_, Aug 21 2011]

%e Triangle starts:

%e 1;

%e 1, 1;

%e 1, 2, 1;

%e 1, 3, 3, 1;

%e 1, 4, 7, 4, 1;

%e 1, 5, 15, 13, 5, 1;

%e 1, 6, 31, 40, 21, 6, 1;

%e ...

%p 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 Cf. A004248, A104879, A104880.

%K easy,nonn,tabl

%O 0,5

%A _Paul Barry_, Mar 28 2005

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Last modified March 20 15:43 EDT 2019. Contains 321345 sequences. (Running on oeis4.)