A177040 Irregular triangle t(n,m) = binomial(m+1,n-m) read by rows floor((n+1)/2) <= m <= n.

1, 1, 2, 1, 3, 1, 3, 4, 1, 6, 5, 1, 4, 10, 6, 1, 10, 15, 7, 1, 5, 20, 21, 8, 1, 15, 35, 28, 9, 1, 6, 35, 56, 36, 10, 1, 21, 70, 84, 45, 11, 1, 7, 56, 126, 120, 55, 12, 1, 28, 126, 210, 165, 66, 13, 1, 8, 84, 252, 330, 220, 78, 14, 1, 36, 210, 462, 495, 286, 91, 15, 1

Offset

0,3

Comments

Row sums are in A052952.

Contains the right half of each row of A030528. - R. J. Mathar, May 19 2013

Links

Table of n, a(n) for n=0..71.

Example

1;
1;
2, 1;
3, 1;
3, 4, 1;
6, 5, 1;
4, 10, 6, 1;
10, 15, 7, 1;
5, 20, 21, 8, 1;
15, 35, 28, 9, 1;
6, 35, 56, 36, 10, 1;
21, 70, 84, 45, 11, 1;
7, 56, 126, 120, 55, 12, 1;
28, 126, 210, 165, 66, 13, 1;
8, 84, 252, 330, 220, 78, 14, 1;
36, 210, 462, 495, 286, 91, 15, 1;

Mathematica

t[n_, m_] := Binomial[m + 1, n - m];
Table[Table[t[n, m], {m, Floor[(n + 1)/2], n}], {n, 0, 15}];
Flatten[%]

Prog

(PARI) T(m, n)=binomial(n+1, m-n) \\ Charles R Greathouse IV, May 19 2013

Crossrefs

Cf. A180987 (read diagonally downwards), A098925, A026729, A085478, A165253

Sequence in context: A081386 A213712 A143802 * A336887 A163313 A337178

Adjacent sequences: A177037 A177038 A177039 * A177041 A177042 A177043

Keyword

nonn,tabf,easy

Author

Roger L. Bagula, May 01 2010

Status

approved