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 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 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

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Last modified June 28 05:40 EDT 2022. Contains 354903 sequences. (Running on oeis4.)