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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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Table of n, a(n) for n=1..62.
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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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(Python3) import math
def binomial(n, m): ...return math.factorial(n)//math.factorial(m)//math.factorial(n-m)
def A001263(n, m): ...return binomial(n-1, m-1)*binomial(n, m-1)//m
def A104711(n, m): ...a =0 ...for k in range(m, n+1): ......a += A001263(k, m) ...return a
print( [A104711(n, m) for n in range(20) for m in range(1, n+1)] ) # R. J. Mathar, Oct 11 2009
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CROSSREFS
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Cf. A014138, A104710, A005585, A000124.
Sequence in context: A186686 A053122 A078812 * A133112 A247239 A198060
Adjacent sequences: A104708 A104709 A104710 * A104712 A104713 A104714
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Mar 19 2005
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EXTENSIONS
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Extended by R. J. Mathar, Oct 11 2009
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STATUS
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approved
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