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A061176 Coefficients of polynomials ((1-x+sqrt(x))^n + (1-x-sqrt(x))^n)/2. 7
1, 1, -1, 1, -1, 1, 1, 0, 0, -1, 1, 2, -5, 2, 1, 1, 5, -15, 15, -5, -1, 1, 9, -30, 41, -30, 9, 1, 1, 14, -49, 77, -77, 49, -14, -1, 1, 20, -70, 112, -125, 112, -70, 20, 1, 1, 27, -90, 126, -117, 117, -126, 90, -27, -1, 1, 35, -105, 90, 45, -131, 45 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,12

COMMENTS

a(n,m)= coefficient of x^m of ((1-x+sqrt(x))^n + (1-x-sqrt(x))^n)/2.

The row polynomial pFe(m+1,x) := sum(a(m+1,k)*x^k,k=0..m+1) is the numerator of the g.f. for the m-th column sequence of A060920, the even part of the bisected Fibonacci triangle.

LINKS

Table of n, a(n) for n=0..61.

FORMULA

a(n, m)= sum(((-1)^(m-j))*binomial(n, 2*j)*binomial(n-2*j, m-j), j=0..m), if 0<= m <= floor(n/2); a(n, m) := ((-1)^n)*a(n, n-m) if floor(n/2) < m <= n; else 0.

EXAMPLE

{1}; {1,-1}; {1,-1,1}; {1,0,0,-1}; ...; pFe(3,x)=1-x^3.

CROSSREFS

A060920, A061177 (companion triangle).

Sequence in context: A064334 A320032 A270061 * A180957 A124780 A108437

Adjacent sequences:  A061173 A061174 A061175 * A061177 A061178 A061179

KEYWORD

sign,easy,tabl

AUTHOR

Wolfdieter Lang, Apr 20 2001

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)