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A104878
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A sum-of-powers number triangle.
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5
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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; internal format)
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OFFSET
| 0,5
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COMMENTS
| Columns are partial sums of the columns of A004248. Row sums are A104879. Diagonal sums are A104880.
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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]
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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]
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CROSSREFS
| Sequence in context: A053534 A104881 A171699 * A196863 A196922 A135597
Adjacent sequences: A104875 A104876 A104877 * A104879 A104880 A104881
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KEYWORD
| easy,nonn,tabl
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 28 2005
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