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A034868 Left half of Pascal's triangle. 15
1, 1, 1, 2, 1, 3, 1, 4, 6, 1, 5, 10, 1, 6, 15, 20, 1, 7, 21, 35, 1, 8, 28, 56, 70, 1, 9, 36, 84, 126, 1, 10, 45, 120, 210, 252, 1, 11, 55, 165, 330, 462, 1, 12, 66, 220, 495, 792, 924, 1, 13, 78, 286, 715, 1287, 1716, 1, 14, 91, 364, 1001, 2002, 3003, 3432, 1, 15 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

T(n,k) = A034869(n,floor(n/2)-k), k = 0..floor(n/2). - Reinhard Zumkeller, Jul 27 2012

LINKS

Reinhard Zumkeller, Rows n=0..150 of triangle, flattened

Index entries for triangles and arrays related to Pascal's triangle

EXAMPLE

1;

1;

1, 2;

1, 3;

1, 4,  6;

1, 5, 10;

1, 6, 15, 20;

...

MATHEMATICA

Flatten[ Table[ Binomial[n, k], {n, 0, 15}, {k, 0, Floor[n/2]}]] (* Robert G. Wilson v, May 28 2005 *)

PROG

(Haskell)

a034868 n k = a034868_tabf !! n !! k

a034868_row n = a034868_tabf !! n

a034868_tabf = map reverse a034869_tabf

-- Reinhard Zumkeller, improved Dec 20 2015, Jul 27 2012

(PARI) for(n=0, 14, for(k=0, floor(n/2), print1(binomial(n, k), ", "); ); print(); ) \\ Indranil Ghosh, Mar 31 2017

(Python)

import math

from sympy import binomial

for n in xrange(0, 15):

....print [binomial(n, k) for k in xrange(0, int(math.floor(n/2)) + 1)] # Indranil Ghosh, Mar 31 2017

CROSSREFS

Cf. A007318, A107430, A062344, A122366, A027306 (row sums).

Cf. A008619.

Cf. A225860.

Cf. A126257.

Cf. A034869 (right half), A014413, A014462, A265848.

Sequence in context: A293892 A295885 A082904 * A050382 A197956 A054072

Adjacent sequences:  A034865 A034866 A034867 * A034869 A034870 A034871

KEYWORD

nonn,tabf,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified September 22 17:05 EDT 2018. Contains 315270 sequences. (Running on oeis4.)