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A143333
Pascal's triangle binomial(n,m) read by rows, all even elements replaced by zero.
5
1, 1, 1, 1, 0, 1, 1, 3, 3, 1, 1, 0, 0, 0, 1, 1, 5, 0, 0, 5, 1, 1, 0, 15, 0, 15, 0, 1, 1, 7, 21, 35, 35, 21, 7, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 9, 0, 0, 0, 0, 0, 0, 9, 1, 1, 0, 45, 0, 0, 0, 0, 0, 45, 0, 1
OFFSET
0,8
COMMENTS
Row sums are A088560.
A047999(n,k) = A057427(T(n,k)). - Reinhard Zumkeller, Oct 24 2010
FORMULA
T(n,m) = A047999(n,m)*A007318(n,m).
EXAMPLE
The triangle starts in row n=0 with columns 0<=m<=n as:
1;
1, 1;
1, 0, 1;
1, 3, 3, 1;
1, 0, 0, 0, 1;
1, 5, 0, 0, 5, 1;
1, 0, 15, 0, 15, 0, 1;
1, 7, 21, 35, 35, 21, 7, 1;
1, 0, 0, 0, 0, 0, 0, 0, 1;
1, 9, 0, 0, 0, 0, 0, 0, 9, 1;
1, 0, 45, 0, 0, 0, 0, 0, 45, 0, 1;
MATHEMATICA
t[n_, m_] = Mod[Binomial[n, m], 2]*Binomial[n, m]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]; Flatten[%]
PROG
(Haskell)
a143333 n k = a143333_tabl !! (n-1) !! (k-1)
a143333_row n = a143333_tabl !! (n-1)
a143333_tabl = zipWith(zipWith (*)) a007318_tabl a047999_tabl
-- Reinhard Zumkeller, Oct 10 2013
CROSSREFS
KEYWORD
nonn,tabl,easy,look
AUTHOR
EXTENSIONS
Offset set to 0 by Reinhard Zumkeller, Oct 21 2010
STATUS
approved