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A142598
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Anti-diagonal triangle sequence of coefficient expansion of the general prime product polynomial: f(x,n)=(1 + t^2)/Product[1 - t^Prime[i + 1], {i, 1, n}].
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0
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1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 2, 1, 1, 0, 1, 1, 0, 2, 1, 0, 1, 0, 1, 1, 0, 2, 1, 1, 1, 1, 0, 1, 1, 0, 2, 1, 2, 2, 1, 1, 0, 1, 1, 0, 2, 1, 2, 2, 1, 0, 1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 2, 1, 1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 3, 2, 1, 1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 3, 2, 2, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,27
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COMMENTS
| Row sums are:
{1, 1, 2, 3, 3, 4, 6, 6, 8, 11, 11, 15, 18, 19, 25}
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FORMULA
| f(x,n)=(1 + t^2)/Product[1 - t^Prime[i + 1], {i, 1, n}]; t(n,m)=expansion(f(x,n)); out_n,m(anti-diagonal)=t(n-m+1,n).
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EXAMPLE
| {1},
{1, 0},
{1, 0, 1},
{1, 0, 1, 1},
{1, 0, 1, 1, 0},
{1, 0, 1, 1, 0, 1},
{1, 0, 1, 1, 0, 2, 1},
{1, 0, 1, 1, 0, 2, 1, 0},
{1, 0, 1, 1, 0, 2, 1, 1, 1},
{1, 0, 1, 1, 0, 2, 1, 2, 2, 1},
{1, 0, 1, 1, 0, 2, 1, 2, 2, 1, 0},
{1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 2, 1},
{1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 3, 2, 1},
{1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 3, 2, 2, 0},
{1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 3, 3, 4, 2, 1}
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MATHEMATICA
| Clear[f, b, a] f[t_, n_] := (1 + t^2)/Product[1 - t^Prime[i + 1], {i, 1, n}]; a = Table[Table[SeriesCoefficient[Series[f[t, m], {t, 0, 30}], n], {n, 0, 30}], {m, 1, 31}]; b = Table[Table[a[[n - m + 1]][[m]], {m, 1, n }], {n, 1, 15}] ; Flatten[b]
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CROSSREFS
| Sequence in context: A076452 A076453 A005590 * A037800 A144411 A138253
Adjacent sequences: A142595 A142596 A142597 * A142599 A142600 A142601
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula and Gary W. Adamson (rlbagulatftn(AT)yahoo.com), Sep 22 2008
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