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A293461
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Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. Product_{i>0} (1 + Sum_{j=1..k} j*x^(j*(2*i-1))).
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2
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1, 1, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 2, 1, 0, 1, 1, 2, 1, 1, 0, 1, 1, 2, 4, 1, 1, 0, 1, 1, 2, 4, 1, 3, 1, 0, 1, 1, 2, 4, 5, 3, 3, 1, 0, 1, 1, 2, 4, 5, 3, 6, 5, 2, 0, 1, 1, 2, 4, 5, 8, 6, 5, 6, 2, 0, 1, 1, 2, 4, 5, 8, 6, 9, 9, 4, 2, 0, 1, 1, 2, 4, 5, 8, 12, 9, 9, 13
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OFFSET
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0,13
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LINKS
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Seiichi Manyama, Antidiagonals n = 0..139, flattened
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, ...
0, 1, 1, 1, 1, ...
0, 0, 2, 2, 2, ...
0, 1, 1, 4, 4, ...
0, 1, 1, 1, 5, ...
0, 1, 3, 3, 3, ...
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MATHEMATICA
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max = 12; A[n_, k_] := SeriesCoefficient[Product[(x*(-(k*x^((2*i - 1)*(k + 1) + 1)) - x^((2*i - 1)*(k + 1) + 1) + k*x^((2*i - 1)*(k + 1) + 2*i) + x^(2*i)))/(x^(2*i) - x)^2 + 1, {i, 1, max}], {x, 0, n}]; Flatten[ Table[ A[n - k, k], {n, 0, max}, {k, n, 0, -1}]] (* Jean-François Alcover, Oct 10 2017 *)
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CROSSREFS
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Columns k=0..3 give A000007, A000700, A293304, A293463.
Rows n=0..1 give A000012, A057427.
Main diagonal gives A102186.
Cf. A290216.
Sequence in context: A037897 A190248 A054070 * A255482 A204172 A126304
Adjacent sequences: A293458 A293459 A293460 * A293462 A293463 A293464
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KEYWORD
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nonn,tabl
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AUTHOR
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Seiichi Manyama, Oct 09 2017
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STATUS
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approved
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