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A061177 Coefficients of polynomials ((1-x+sqrt(x))^(n+1) - (1-x-sqrt(x))^(n+1))/(2*sqrt(x)). 6
1, 2, -2, 3, -5, 3, 4, -8, 8, -4, 5, -10, 11, -10, 5, 6, -10, 6, -6, 10, -6, 7, -7, -14, 29, -14, -7, 7, 8, 0, -56, 120, -120, 56, 0, -8, 9, 12, -126, 288, -365, 288, -126, 12, 9, 10, 30, -228, 540, -770, 770, -540, 228, -30, -10, 11, 55, -363, 858 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The row polynomial pFo(m,x) := sum(a(m,k)*x^k,k=0..m) is the numerator of the g.f. for the m-th column sequence of A060921, the odd part of the bisected Fibonacci triangle.

LINKS

Table of n, a(n) for n=0..58.

FORMULA

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

a(n, m)= sum(((-1)^(m-j))*binomial(n+1, 2*j+1)*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}; {2,-2}; {3,-5,3}; {4,-8,8,-4}; ...; pFo(2,x)=3-5*x+3*x^2.

CROSSREFS

A060921, A061176 (companion triangle).

Sequence in context: A204000 A132071 A334923 * A129312 A115262 A128141

Adjacent sequences:  A061174 A061175 A061176 * A061178 A061179 A061180

KEYWORD

sign,easy,tabl

AUTHOR

Wolfdieter Lang, Apr 20 2001

STATUS

approved

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Last modified September 24 04:19 EDT 2020. Contains 337317 sequences. (Running on oeis4.)