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A080381
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Triangle read by rows: GCD[C[n,Floor[n/2]],C[n,i], i=0,...n; greatest common divisor of binomial coefficients and corresponding central binomial coefficient.
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5
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1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 2, 6, 2, 1, 1, 5, 10, 10, 5, 1, 1, 2, 5, 20, 5, 2, 1, 1, 7, 7, 35, 35, 7, 7, 1, 1, 2, 14, 14, 70, 14, 14, 2, 1, 1, 9, 18, 42, 126, 126, 42, 18, 9, 1, 1, 2, 9, 12, 42, 252, 42, 12, 9, 2, 1, 1, 11, 11, 33, 66, 462, 462, 66, 33, 11, 11, 1, 1, 12, 66, 44, 33, 132
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OFFSET
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0,5
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COMMENTS
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The matrix inverse starts
1;
-1,1;
1,-2,1;
-1,3,-3,1;
-3,4,0,-2,1;
19,-35,20,0,-5,1;
-7,-2,15,-10,5,-2,1;
55,21,-147,105,-35,7,-7,1
-67,180,-168,56,0,0,0,-2,1; - R. J. Mathar, Mar 21 2013
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LINKS
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Table of n, a(n) for n=0..83.
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EXAMPLE
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Triangle begins:
1
1 1
1 2 1
1 3 3 1
1 2 6 2 1
1 5 10 10 5 1
1 2 5 20 5 2 1
1 7 7 35 35 7 7 1
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MAPLE
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A080381 := proc(n, k)
if k < 0 or k > n then
0;
else
igcd(binomial(n, floor(n/2)), binomial(n, k)) ;
end if;
end proc: # R. J. Mathar, Mar 21 2013
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MATHEMATICA
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Table[Table[GCD[Binomial[n, j], Binomial[n, Floor[n/2]]], {j, 0, n}], {n, 1, 10}]
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CROSSREFS
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Cf. A007318, A001405.
Sequence in context: A132422 A065133 A204087 * A080396 A155582 A169946
Adjacent sequences: A080378 A080379 A080380 * A080382 A080383 A080384
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KEYWORD
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nonn,tabl
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Mar 12 2003
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STATUS
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approved
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