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A109409
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Coefficients of polynomials triangular sequence produced by removing primes from the odd numbers in A028338.
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0
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1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 0, 9, 10, 1, 0, 0, 0, 0, 9, 10, 1, 0, 0, 0, 0, 0, 9, 10, 1, 0, 0, 0, 0, 0, 135, 159, 25, 1, 0, 0, 0, 0, 0, 0, 135, 159, 25, 1, 0, 0, 0, 0, 0, 0, 0, 135, 159, 25, 1, 0, 0, 0, 0, 0, 0, 0, 2835, 3474, 684, 46, 1
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OFFSET
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1,19
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COMMENTS
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The row sums also appear to be new: b = Flatten[Join[{{1}}, Table[Apply[Plus, Abs[CoefficientList[Product[x + g[n], {n, 0, m}], x]]], {m, 0, 10}]]] {1, 2, 2, 2, 2, 20, 20, 20, 320, 320, 320, 7040} Since the row sum of A028338 is the double factorial A000165: this result seems to be a factorization of the double factorial numbers by relatively sparse nonprime odd numbers. It might be better to reverse the order of the coefficients to get the higher powers first.
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LINKS
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Table of n, a(n) for n=1..78.
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FORMULA
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p[n]=Product[If[PrimeQ[2*n+1]==false,x+(2*n+1),x] a(n) =CoefficientList[p[n],x]
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EXAMPLE
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{1},
{1, 1},
{0, 1, 1},
{0, 0, 1, 1},
{0, 0, 0, 1, 1},
{0, 0, 0, 9, 10, 1},
{0, 0, 0, 0, 9, 10, 1},
{0, 0, 0, 0, 0, 9, 10, 1}
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MATHEMATICA
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a = Join[{{1}}, Table[CoefficientList[Product[x + g[n], {n, 0, m}], x], {m, 0, 10}]]; Flatten[a]
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CROSSREFS
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Cf. A028338, A000165, A039757.
Sequence in context: A220450 A318147 A324663 * A262551 A160563 A158286
Adjacent sequences: A109406 A109407 A109408 * A109410 A109411 A109412
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KEYWORD
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nonn,uned
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AUTHOR
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Roger L. Bagula, May 19 2007
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STATUS
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approved
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