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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A091043 Normalized triangle of odd numbered entries of even numbered rows of Pascal's triangle A007318. 11
1, 1, 1, 3, 10, 3, 1, 7, 7, 1, 5, 60, 126, 60, 5, 3, 55, 198, 198, 55, 3, 7, 182, 1001, 1716, 1001, 182, 7, 1, 35, 273, 715, 715, 273, 35, 1, 9, 408, 4284, 15912, 24310, 15912, 4284, 408, 9, 5, 285, 3876, 19380, 41990, 41990, 19380, 3876, 285, 5, 11, 770, 13167, 85272 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

b(n)= A006519(n), with b(n) defined in the formula. For every odd n b(n)=1.

The row polynomials Po(n,x) := 2*b(n)*sum(a(n,m)*x^m,m=0..n-1), n>=1, appear as numerators of the generating functions for the odd numbered column sequences of array A034870. b(n) is defined in the formula below.

LINKS

Table of n, a(n) for n=1..59.

W. Lang, First 9 rows.

FORMULA

a(n, m)= binomial(2*n, 2*m+1)/(2*b(n)), n>=m+1>=1, else 0, with b(n) := GCD(seq(binomial(2*n, 2*m+1)/2, m=0..n-1)), where GCD denotes the greatest common divisor of a set of numbers (here one half of the odd numbered entries in the even numbered rows of Pascal's triangle). It suffices to consider m=0..floor((n-1)/2) due to symmetry.

EXAMPLE

[1];[1,1];[3,10,3];[1,7,7,1];[5,60,126,60,5];...

n=3: GCD(3,10,3)=GCD(3,10)=1=b(3)=A006519(3); n=4: GCD(4,28,28,4)=GCD(4,28)=4=b(4)=A006519(4).

CROSSREFS

Sequence in context: A179397 A111272 A124692 * A321118 A167790 A010708

Adjacent sequences:  A091040 A091041 A091042 * A091044 A091045 A091046

KEYWORD

nonn,easy,tabl

AUTHOR

Wolfdieter Lang, Jan 23 2004

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 21 06:01 EDT 2019. Contains 328291 sequences. (Running on oeis4.)