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A141680
Triangle read by rows: T(n,m) = (n/m)*binomial(n,m) if m divides n, otherwise 0.
2
1, 4, 1, 9, 0, 1, 16, 12, 0, 1, 25, 0, 0, 0, 1, 36, 45, 40, 0, 0, 1, 49, 0, 0, 0, 0, 0, 1, 64, 112, 0, 140, 0, 0, 0, 1, 81, 0, 252, 0, 0, 0, 0, 0, 1, 100, 225, 0, 0, 504, 0, 0, 0, 0, 1
OFFSET
1,2
COMMENTS
Row sums are: 1, 5, 10, 29, 26, 122, 50, 317, 334, 830, ... A105862.
FORMULA
T(n,m) = A126988(n,m)*binomial(n,m).
T(n,1) = n^2. T(n,n) = 1. T(2n,2) = A015237(n).
EXAMPLE
1;
4, 1;
9, 0, 1;
16, 12, 0, 1;
25, 0, 0, 0, 1;
36, 45, 40, 0, 0, 1;
49, 0, 0, 0, 0, 0, 1;
64, 112, 0, 140, 0, 0, 0, 1;
81, 0, 252, 0, 0, 0, 0, 0, 1;
100, 225, 0, 0, 504, 0, 0, 0, 0, 1;
MATHEMATICA
t[n_, m_] = If[Mod[n, m] == 0, n/m, 0]*Binomial[n, m]; Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}]; Flatten[%]
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
STATUS
approved