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Search: id:A061186
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| A061186 |
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Staircase of coefficients of polynomials used for column g.f.s of triangle A060923. |
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+0
6
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| 1, 1, 1, 1, 11, -11, 4, 1, 30, -6, -23, 12, 1, 58, 123, -278, 193, -72, 16, 1, 95, 565, -715, -145, 601, -360, 80, 1, 141, 1590, 89, -5226, 6441, -3659, 1260, -336, 64, 1, 196, 3549, 6797, -22099, 12369, 9156, -15791, 9492
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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a(n,m) is coefficient of x^m of polynomial pLe(n,x) := (((1+x)+(3-2*x)*sqrt(x))^n + ((1+x)-(3-2*x)*sqrt(x))^n)/2 of degree n+floor(n/2)= A032766(n). pLe(n,x)= sum(binomial(n,2*j)*(1+x)^(n-2*j)*(3-2*x)^(2*j)*x^j,j=0..floor(n/2)), n >= 1; pLe(0,x)=1.
pLe(m+1,x) is the numerator polynomial of the g.f. for column m >= 0 of the triangle A060923 (even part of bisection of Lucas triangle).
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FORMULA
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a(n, m)=sum(((-9/2)^j*binomial(n, 2*j)*sum((-3/2)^(k-m)*binomial(n-2*j, k)*binomial(2*j, m-k-j), k=max(0, (m-3*j))..(n-2*j))), j=0..floor(n/2)), 0<= m <= n+floor(n/2); else 0.
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EXAMPLE
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{1}; {1,1}; {1,11,-11,4}; ...; pLe(2,x)= 1+11*x-11*x^2+4*x^3.
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CROSSREFS
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A061187 (companion staircase).
Sequence in context: A167262 A014459 A046609 this_sequence A135684 A126610 A087380
Adjacent sequences: A061183 A061184 A061185 this_sequence A061187 A061188 A061189
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KEYWORD
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sign,easy,tabf
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Apr 20 2001
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