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A235790
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Triangle read by rows: T(n,k) = 2^k*A116608(n,k), n>=1, k>=1.
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13
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2, 4, 4, 4, 6, 8, 4, 20, 8, 24, 8, 4, 44, 16, 8, 52, 40, 6, 68, 80, 8, 88, 120, 16, 4, 108, 200, 32, 12, 116, 296, 80, 4, 148, 416, 160, 8, 176, 536, 320, 8, 176, 776, 480, 32, 10, 220, 936, 832, 64, 4, 236, 1232, 1232, 160, 12, 272, 1472, 1872, 320
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OFFSET
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1,1
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COMMENTS
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It appears that T(n,k) is the number of overpartitions of n having k distinct parts. (This is true by definition, Joerg Arndt, Jan 20 2014).
Row n has length A003056(n) hence the first element of column k is in row A000217(k).
The first element of column k is A000079(k).
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LINKS
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EXAMPLE
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Triangle begins:
2;
4;
4, 4;
6, 8;
4, 20;
8, 24, 8;
4, 44, 16;
8, 52, 40;
6, 68, 80;
8, 88, 120, 16;
4, 108, 200, 32;
12, 116, 296, 80;
4, 148, 416, 160;
8, 176, 536, 320;
8, 176, 776, 480, 32;
10, 220, 936, 832, 64;
4, 236, 1232, 1232, 160;
12, 272, 1472, 1872, 320;
4, 284, 1880, 2592, 640;
12, 324, 2216, 3632, 1152;
8, 328, 2704, 4944, 1856, 64;
...
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MAPLE
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b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
expand(b(n, i-1)+add(x*b(n-i*j, i-1), j=1..n/i))))
end:
T:= n->(p->seq(2^i*coeff(p, x, i), i=1..degree(p)))(b(n$2)):
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MATHEMATICA
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b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Expand[b[n, i-1] + Sum[x*b[n-i*j, i-1], {j, 1, n/i}]]]]; T[n_] := Function[p, Table[2^i * Coefficient[p, x, i], {i, 1, Exponent[p, x]}]][b[n, n]]; Table[T[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, Oct 20 2016, after Alois P. Heinz *)
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CROSSREFS
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Cf. A000217, A003056, A116608, A196020, A211971, A235792, A235793, A235797, A235798, A235999, A236000, A236001.
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KEYWORD
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AUTHOR
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STATUS
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approved
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