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A117195
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Triangle read by rows: T(n,k) = number of partitions into distinct parts having rank k, 0<=k<n.
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6
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1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 2, 1, 1, 1, 0, 1, 1, 0, 2, 1, 2, 1, 1, 1, 0, 1, 0, 1, 1, 2, 2, 2, 1, 1, 1, 0, 1, 0, 1, 2, 2, 2, 2, 2, 1, 1, 1, 0, 1, 0, 1, 1, 3, 2, 3, 2, 2, 1, 1, 1, 0, 1, 0, 1, 2, 2, 4, 2, 3, 2, 2, 1, 1, 1, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,40
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COMMENTS
| T(n,0) = A010054(n), T(n,1) = 1-A010054(n) for n>1;
A000009(n) = Sum(T(n,k): 0<=k<n);
A117192(n) = Sum(T(n,k)*(1 - k mod 2): 0<=k<n);
A117193(n) = Sum(T(n,k)*(k mod 2): 0<=k<n);
A117194(n) = Sum(T(n,k)*(1 - k mod 2): 0<k<n);
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LINKS
| Alois P. Heinz, Rows n = 1..141, flattened
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EXAMPLE
| T(12,0) = #{} = 0,
T(12,1) = #{5+4+2+1} = 1,
T(12,2) = #{6+3+2+1, 5+4+3} = 2,
T(12,3) = #{6+5+1, 6+4+2} = 2,
T(12,4) = #{7+4+1, 7+3+2} = 2,
T(12,5) = #{8+3+1, 7+5} = 2,
T(12,6) = #{9+2+1, 8+4} = 2,
T(12,7) = #{9+3} = 1,
T(12,8) = #{10+2} = 1,
T(12,9) = #{11+1} = 1,
T(12,10) = #{} = 0,
T(12,11) = #{12} = 1.
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MAPLE
| b:= proc(n, i, k) option remember;
if n<0 or k<0 then []
elif n=0 then [0$k, 1]
elif i<1 then []
else zip ((x, y)-> x+y, b(n, i-1, k), b(n-i, i-1, k-1), 0)
fi
end:
T:= proc(n) local j, r;
r:= [];
for j from 0 to n do
r:= zip ((x, y)-> x+y, r, b(n-j, j-1, j-1), 0)
od; r[]
end:
seq (T(n), n=1..20); # Alois P. Heinz, Aug 29 2011
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CROSSREFS
| Cf. A063995, A105806.
Sequence in context: A037907 A037801 A053252 * A156606 A194087 A107034
Adjacent sequences: A117192 A117193 A117194 * A117196 A117197 A117198
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KEYWORD
| nonn,tabl
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AUTHOR
| Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Mar 03 2006
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