A157694 Triangle read by rows: the Pascal triangle A007318 with all elements replaced by 1 which do not equal the central binomial coefficients.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 1, 6, 1, 1, 1, 1, 10, 10, 1, 1, 1, 1, 1, 20, 1, 1, 1, 1, 1, 1, 35, 35, 1, 1, 1, 1, 1, 1, 1, 70, 1, 1, 1, 1, 1, 1, 1, 1, 126, 126, 1, 1, 1, 1, 1, 1, 1, 1, 1, 252, 1, 1, 1, 1, 1

Offset

0,5

Comments

Row sums are {1, 2, 4, 8, 10, 24, 26, 76, 78, 260, 262,...}.

Links

Table of n, a(n) for n=0..65.

Formula

t(n,m)= binomial(n,[n/2]) if this equals binomial(n,m), else 1.

Example

{1},
{1, 1},
{1, 2, 1},
{1, 3, 3, 1},
{1, 1, 6, 1, 1},
{1, 1, 10, 10, 1, 1},
{1, 1, 1, 20, 1, 1, 1},
{1, 1, 1, 35, 35, 1, 1, 1},
{1, 1, 1, 1, 70, 1, 1, 1, 1},
{1, 1, 1, 1, 126, 126, 1, 1, 1, 1},
{1, 1, 1, 1, 1, 252, 1, 1, 1, 1, 1}

Mathematica

Clear[t, n, m];
t[n_, m_] = If[ Binomial[n, m] == Binomial[n, Floor[n/2]], Binomial[n, Floor[n/2]], 1];
Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}];
Flatten[%]

Crossrefs

Sequence in context: A026082 A117185 A129181 * A271187 A093557 A098802

Adjacent sequences: A157691 A157692 A157693 * A157695 A157696 A157697

Keyword

nonn,easy,tabl

Author

Roger L. Bagula, Mar 04 2009

Extensions

Edited by the Associate Editors of the OEIS, Apr 10 2009

Status

approved