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

1,19

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

Table of n, a(n) for n=1..78.

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