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 A109409 Coefficients of polynomials triangular sequence produced by removing primes from the odd numbers in A028338. 0

%I

%S 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,

%T 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,

%U 135,159,25,1,0,0,0,0,0,0,0,2835,3474,684,46,1

%N Coefficients of polynomials triangular sequence produced by removing primes from the odd numbers in A028338.

%C 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.

%F p[n]=Product[If[PrimeQ[2*n+1]==false,x+(2*n+1),x] a(n) =CoefficientList[p[n],x]

%e {1},

%e {1, 1},

%e {0, 1, 1},

%e {0, 0, 1, 1},

%e {0, 0, 0, 1, 1},

%e {0, 0, 0, 9, 10, 1},

%e {0, 0, 0, 0, 9, 10, 1},

%e {0, 0, 0, 0, 0, 9, 10, 1}

%t a = Join[{{1}}, Table[CoefficientList[Product[x + g[n], {n, 0, m}], x], {m, 0, 10}]]; Flatten[a]

%Y Cf. A028338, A000165, A039757.

%K nonn,uned

%O 1,19

%A _Roger L. Bagula_, May 19 2007

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