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Search: id:A102716
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| A102716 |
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Triangle read by rows: T(n,k) = sigma(binom(n,k)) (0<=k<=n), where sigma(m) is the sum of the positive divisors of m. |
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+0
1
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| 1, 1, 1, 1, 3, 1, 1, 4, 4, 1, 1, 7, 12, 7, 1, 1, 6, 18, 18, 6, 1, 1, 12, 24, 42, 24, 12, 1, 1, 8, 32, 48, 48, 32, 8, 1, 1, 15, 56, 120, 144, 120, 56, 15, 1, 1, 13, 91, 224, 312, 312, 224, 91, 13, 1, 1, 18, 78, 360, 576, 728, 576, 360, 78, 18, 1, 1, 12, 72, 288, 864, 1152, 1152, 864
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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Row n contains n+1 terms. Row sums yield A074801. T(2n,n)=A067819(n)
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LINKS
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T. D. Noe, Rows n=0..100 of triangle, flattened
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FORMULA
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T(n, k)=sigma(binom(n, k)) (0<=k<=n).
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EXAMPLE
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T(6,3)=42 because the sum of the divisors of binom(6,3)=20 is 1+2+4+5+10+20=42.
Triangle begins:
1;
1,1;
1,3,1;
1,4,4,1;
1,7,12,7,1;
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MAPLE
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with(numtheory): T:=(n, k)->sigma(binomial(n, k)): for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A074801, A067819.
Sequence in context: A026648 A026747 A026374 this_sequence A134510 A124020 A124234
Adjacent sequences: A102713 A102714 A102715 this_sequence A102717 A102718 A102719
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KEYWORD
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nonn,tabl
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AUTHOR
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Emeric Deutsch (deutsch(AT)duke.poly.edu), Feb 06 2005
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