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A118980
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Triangle read by rows: rows = inverse binomial transforms of columns of A309220.
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3
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1, 2, 1, 6, 5, 2, 14, 22, 18, 6, 34, 85, 118, 84, 24, 82, 311, 660, 780, 480, 120, 198, 1100, 3380, 5964, 6024, 3240, 720, 478, 3809, 16380, 40740, 60480, 52920, 25200, 5040, 1154, 13005, 76518, 258804, 531864, 676080, 519840, 221760, 40320, 2786, 43978, 348462, 1564314, 4286880, 7444800, 8240400
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OFFSET
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1,2
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COMMENTS
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1, 2, 6, 14, 34, ...
1, 3, 11, 36, 119, ...
1, 4, 18, 76, 322, ...
1, 5, 27, 140, 727, ...
1, 6, 38, 234, 1442, ...
1, 7, 51, 364, 2599, ...
1, 8, 66, 536, 4354, ...
...
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LINKS
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EXAMPLE
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First few rows of the triangle:
1;
2, 1;
6, 5, 2;
14, 22, 18, 6;
34, 85, 118, 84, 24;
82, 311, 660, 780, 480, 120;
...
Column 3 of A309220 = (6, 11, 18, 27, 38, 51, ...), whose inverse binomial transform is (6, 5, 2).
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MAPLE
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with(transforms);
M := 12;
T := [1];
S := series((1 + x^2)/(1-x-x^2 + x*y), x, 120):
for n from 1 to M do
R2 := expand(coeff(S, x, n));
R3 := [seq(abs(coeff(R2, y, n-i)), i=0..n)];
f := k-> add( R3[i]*k^(n-i+1), i=1..nops(R3) ):
s1 := [seq(f(i), i=1..3*n)];
s2 := BINOMIALi(s1);
s3 := [seq(s2[i], i=1..n+1)];
T := [op(T), op(s3)];
od:
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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