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 A109409 Coefficients of polynomials triangular sequence produced by removing primes from the odd numbers in A028338. 0
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,19 COMMENTS 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. LINKS FORMULA p[n]=Product[If[PrimeQ[2*n+1]==false,x+(2*n+1),x] a(n) =CoefficientList[p[n],x] EXAMPLE {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} MATHEMATICA a = Join[{{1}}, Table[CoefficientList[Product[x + g[n], {n, 0, m}], x], {m, 0, 10}]]; Flatten[a] CROSSREFS Cf. A028338, A000165, A039757. Sequence in context: A220450 A318147 A324663 * A262551 A160563 A158286 Adjacent sequences:  A109406 A109407 A109408 * A109410 A109411 A109412 KEYWORD nonn,uned AUTHOR Roger L. Bagula, May 19 2007 STATUS approved

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Last modified August 10 00:32 EDT 2022. Contains 356026 sequences. (Running on oeis4.)