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A059328
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Table T(n,k) = T(n - 1,k) + T(n,k - 1) + T(n - 1,k)*T(n,k - 1) starting with T(0,0)=1, read by antidiagonals.
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1
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1, 1, 1, 1, 3, 1, 1, 7, 7, 1, 1, 15, 63, 15, 1, 1, 31, 1023, 1023, 31, 1, 1, 63, 32767, 1048575, 32767, 63, 1, 1, 127, 2097151, 34359738367, 34359738367, 2097151, 127, 1, 1, 255, 268435455, 72057594037927935, 1180591620717411303423
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OFFSET
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0,5
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COMMENTS
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In binary representation T(n,k) is the concatenation of T(n-1,k-1) and T(n-1,k), 0<k<n. - Reinhard Zumkeller, Jan 23 2003
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LINKS
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FORMULA
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T(n, k) = 2^C(n+k, n)-1; a(n) = 2^A007318(n)-1.
If U(n, k) := 1 + T(n, k), then U(n, k) = U(n-1, k) * U(n, k-1). - Michael Somos, Jan 07 2017
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MATHEMATICA
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Table[2^(Binomial[n, k]) - 1, {n, 0, 5}, {k, 0, n}] (* G. C. Greubel, Jan 07 2017 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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