A111505 Right half of Pascal's triangle (A007318) with zeros.

1, 0, 1, 0, 2, 1, 0, 0, 3, 1, 0, 0, 6, 4, 1, 0, 0, 0, 10, 5, 1, 0, 0, 0, 20, 15, 6, 1, 0, 0, 0, 0, 35, 21, 7, 1, 0, 0, 0, 0, 70, 56, 28, 8, 1, 0, 0, 0, 0, 0, 126, 84, 36, 9, 1, 0, 0, 0, 0, 0, 252, 210, 120, 45, 10, 1, 0, 0, 0, 0, 0, 0, 462, 330, 165

Offset

0,5

Comments

A034869 is the version without zeros.

Links

Table of n, a(n) for n=0..74.

Formula

Sum_{n, n>=k} T(n, k) = A001700(k).

Sum_{k =0..2*n} T(2*n, k) = A032443(n).

Sum_{k=0..2*n+1} T(2*n+1, k) = 4^n = A000302(n).

Sum_{k=0..2*n} T(2*n, k)^2 = A036910(n).

Sum_{k=0..2*n+1} T(2*n+1, k)^2 = C(4*n+1, 2*n) = A002458(n) . Paul D. Hanna

Example

Triangle begins:
1;
0, 1;
0, 2, 1;
0, 0, 3, 1;
0, 0, 6, 4, 1;
0, 0, 0, 10, 5, 1;
0, 0, 0, 20, 15, 6, 1;
0, 0, 0, 0, 35, 21, 7, 1;
0, 0, 0, 0, 70, 56, 28, 8, 1;
0, 0, 0, 0, 0, 126, 84, 36, 9, 1;
0, 0, 0, 0, 0, 252, 210, 120, 45, 10, 1;
0, 0, 0, 0, 0, 0, 462, 330, 165, 55, 11, 1;
0, 0, 0, 0, 0, 0, 924, 792, 495, 220, 66, 12, 1;
0, 0, 0, 0, 0, 0, 0, 1716, 1287, 715, 286, 78, 13, 1;
0, 0, 0, 0, 0, 0, 0, 3432, 3003, 2002, 1001, 364, 91, 14, 1;

Crossrefs

Cf. A007318, A034869, A094527, A111418.

Sequence in context: A105593 A029371 A114374 * A109264 A322393 A294265

Adjacent sequences: A111502 A111503 A111504 * A111506 A111507 A111508

Keyword

nonn,tabl

Author

Philippe Deléham, Nov 16 2005

Status

approved