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

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

Offset: 1

Author

Roger L. Bagula, May 19 2007

Keywords

• nonn
• uned

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.

Examples

			{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}
		

Crossrefs

Cf. A028338, A000165, A039757.

Programs

Mathematica

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

Formula

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