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A089818
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T(n,k) = number of subsets of {1,..., n} containing exactly k primes, triangle read by rows, 0<=k<n.
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4
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2, 2, 2, 2, 4, 2, 4, 8, 4, 0, 4, 12, 12, 4, 0, 8, 24, 24, 8, 0, 0, 8, 32, 48, 32, 8, 0, 0, 16, 64, 96, 64, 16, 0, 0, 0, 32, 128, 192, 128, 32, 0, 0, 0, 0, 64, 256, 384, 256, 64, 0, 0, 0, 0, 0, 64, 320, 640, 640, 320, 64, 0, 0, 0, 0, 0, 128, 640, 1280, 1280, 640, 128, 0, 0, 0, 0, 0
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| T(n,k) = T(n, A000720(n)-k) for 0<=k<=A000720(n);
T(n,k) = 0 iff k > A000720(n);
A089819(n) = T(n,0); A089821(n) = T(n,1) for n>1; A089822(n) = T(n,2) for n>2;
A089820(n) = Sum(T(n,k): 1<=k<=A000720(n));
T(n,k) = A007318(A000720(n),k) * A000079(n-A000720(n)).
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FORMULA
| T(n, k) = binomial(pi(n), k)*2^(n-pi(n)), with pi = A000720.
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CROSSREFS
| Cf. A000040.
Sequence in context: A037445 A186643 A003036 * A067025 A049047 A037088
Adjacent sequences: A089815 A089816 A089817 * A089819 A089820 A089821
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KEYWORD
| nonn,tabl
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Nov 12 2003
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