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 A034868 Left half of Pascal's triangle. 16

%I

%S 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,

%T 126,1,10,45,120,210,252,1,11,55,165,330,462,1,12,66,220,495,792,924,

%U 1,13,78,286,715,1287,1716,1,14,91,364,1001,2002,3003,3432,1,15

%N Left half of Pascal's triangle.

%C T(n,k) = A034869(n,floor(n/2)-k), k = 0..floor(n/2). - _Reinhard Zumkeller_, Jul 27 2012

%H Reinhard Zumkeller, <a href="/A034868/b034868.txt">Rows n=0..150 of triangle, flattened</a>

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

%e 1;

%e 1;

%e 1, 2;

%e 1, 3;

%e 1, 4, 6;

%e 1, 5, 10;

%e 1, 6, 15, 20;

%e ...

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

%o a034868 n k = a034868_tabf !! n !! k

%o a034868_row n = a034868_tabf !! n

%o a034868_tabf = map reverse a034869_tabf

%o -- _Reinhard Zumkeller_, improved Dec 20 2015, Jul 27 2012

%o (PARI) for(n=0, 14, for(k=0, floor(n/2), print1(binomial(n, k),", ");); print();) \\ _Indranil Ghosh_, Mar 31 2017

%o (Python)

%o import math

%o from sympy import binomial

%o for n in range(15):

%o print([binomial(n, k) for k in range(int(math.floor(n/2)) + 1)]) # _Indranil Ghosh_, Mar 31 2017

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

%Y Cf. A008619.

%Y Cf. A225860.

%Y Cf. A126257.

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

%K nonn,tabf,easy

%O 0,4

%A _N. J. A. Sloane_

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Last modified April 19 00:18 EDT 2021. Contains 343098 sequences. (Running on oeis4.)