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A104711
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Triangle T(n,m) = sum_{k=m..n} A001263(k,m).
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2
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1, 2, 1, 3, 4, 1, 4, 10, 7, 1, 5, 20, 27, 11, 1, 6, 35, 77, 61, 16, 1, 7, 56, 182, 236, 121, 22, 1, 8, 84, 378, 726, 611, 218, 29, 1, 9, 120, 714, 1902, 2375, 1394, 365, 37, 1, 10, 165, 1254, 4422, 7667, 6686, 2885, 577, 46, 1, 11, 220, 2079, 9372, 21527, 26090, 16745
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OFFSET
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1,2
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COMMENTS
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This summation over columns of the Narayana triangle could also be defined as a multiplication
of the Narayana triangle from the left by the lower-left triangle represented by the all-1 sequence A000012.
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LINKS
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FORMULA
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Row sums: sum_{m=1..n} T(n,m) = A014138(n).
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EXAMPLE
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First few rows of the triangle are:
1;
2, 1;
3, 4, 1;
4, 10, 7, 1;
5, 20, 27, 11, 1;
6, 35, 77, 61, 16, 1;
...
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PROG
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(Python)
from sympy import binomial
return binomial(n-1, m-1)*binomial(n, m-1)//m
a = 0
for k in range(m, n+1):
return a
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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