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A111505 Right half of Pascal's triangle (A007318) with zeros. 0
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified October 1 08:39 EDT 2020. Contains 337442 sequences. (Running on oeis4.)