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A104878 A sum-of-powers number triangle. 5
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, 121, 85, 31, 7, 1, 1, 8, 127, 364, 341, 156, 43, 8, 1, 1, 9, 255, 1093, 1365, 781, 259, 57, 9, 1, 1, 10, 511, 3280, 5461, 3906, 1555, 400, 73, 10, 1, 1, 11, 1023, 9841, 21845 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

LINKS

Table of n, a(n) for n=0..70.

FORMULA

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

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

T(n,k) = A069777(n+1,k)/A069777(n,k). [Johannes W. Meijer, Aug 21 2011]

EXAMPLE

Triangle starts:

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;

...

MAPLE

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

CROSSREFS

Cf. A004248, A104879, A104880.

Sequence in context: A053534 A104881 A171699 * A196863 A196922 A135597

Adjacent sequences:  A104875 A104876 A104877 * A104879 A104880 A104881

KEYWORD

easy,nonn,tabl

AUTHOR

Paul Barry, Mar 28 2005

STATUS

approved

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Last modified February 16 18:53 EST 2019. Contains 320165 sequences. (Running on oeis4.)