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A101508
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Product of binomial matrix and the Mobius matrix A051731.
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5
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1, 2, 1, 4, 2, 1, 8, 4, 3, 1, 16, 8, 6, 4, 1, 32, 16, 11, 10, 5, 1, 64, 32, 21, 20, 15, 6, 1, 128, 64, 42, 36, 35, 21, 7, 1, 256, 128, 85, 64, 70, 56, 28, 8, 1, 512, 256, 171, 120, 127, 126, 84, 36, 9, 1, 1024, 512, 342, 240, 220, 252, 210, 120, 45, 10, 1, 2048, 1024, 683, 496, 385, 463, 462, 330, 165, 55, 11, 1
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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Number triangle T(n, k)=sum{i=0..n, if(mod(i+1, k+1)=0, binomial(n, i), 0)};
Rows have g.f. x^k/((1-x)^(k+1)-x^(k+1)).
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EXAMPLE
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Rows begin
1;
2,1;
4,2,1;
8,4,3,1;
16,8,6,4,1;
...
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MAPLE
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a := 0 ;
for i from 0 to n do
if modp(i+1, k+1) = 0 then
a := a+binomial(n, i) ;
end if;
end do:
return a;
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MATHEMATICA
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t[n_, k_] := Sum[If[Mod[i + 1, k + 1] == 0, Binomial[n, i], 0], {i, 0, n}]; Table[t[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 24 2014 *)
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PROG
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(PARI) T(n, k)=sum(i=0, n, if((i+1)%(k+1)==0, binomial(n, i)) \\ M. F. Hasler, Mar 05 2017
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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