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A034868
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Left half of Pascal's triangle.
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16
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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)
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OFFSET
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0,4
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LINKS
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FORMULA
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EXAMPLE
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1;
1;
1, 2;
1, 3;
1, 4, 6;
1, 5, 10;
1, 6, 15, 20;
...
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MATHEMATICA
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Flatten[ Table[ Binomial[n, k], {n, 0, 15}, {k, 0, Floor[n/2]}]] (* Robert G. Wilson v, May 28 2005 *)
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PROG
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(Haskell)
a034868 n k = a034868_tabf !! n !! k
a034868_row n = a034868_tabf !! n
a034868_tabf = map reverse a034869_tabf
(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 range(15):
print([binomial(n, k) for k in range(int(math.floor(n/2)) + 1)]) # Indranil Ghosh, Mar 31 2017
(Python)
from itertools import count, islice
def A034868_gen(): # generator of terms
yield from (s:=(1, ))
for i in count(0):
yield from (s:=(1, )+tuple(s[j]+s[j+1] for j in range(len(s)-1)) + ((s[-1]<<1, ) if i&1 else ()))
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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STATUS
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approved
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