login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 10 11:39 EST 2016. Contains 279001 sequences.