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A109771
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G.f.: sqrt(1+6*x+x^2).
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0
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1, 3, -4, 12, -44, 180, -788, 3612, -17116, 83172, -412196, 2075436, -10586892, 54595476, -284157492, 1490774076, -7875206076, 41854313412, -223636052036, 1200637707852, -6473448634348, 35037238641780, -190299310403924, 1036863750837852, -5665846701859484
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| G.f. = square root of weight enumerator of [4,3,2] even weight code.
a(n) gives the row sums of the coefficient array for the family Gegenbauer_C(n,-1/2,-2x-1). [From Paul Barry (pbarry(AT)wit.ie), Apr 20 2009]
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LINKS
| N. Heninger, E. M. Rains and N. J. A. Sloane, On the Integrality of n-th Roots of Generating Functions, J. Combinatorial Theory, Series A, 113 (2006), 1732-1745.
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FORMULA
| a(n)=(-1)^n*sum{k=0..n, C(n+k-2,n-k)*C(2k,k)/(1-2k)}=(-1)^n*sum{k=0..n, C(n+k-2,n-k)*A002420(k)}; [From Paul Barry (pbarry(AT)wit.ie), Apr 20 2009]
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EXAMPLE
| 1+3*x-4*x^2+12*x^3-44*x^4+180*x^5-788*x^6+3612*x^7-...
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CROSSREFS
| Sequence in context: A000208 A079154 A101716 * A052626 A122903 A059792
Adjacent sequences: A109768 A109769 A109770 * A109772 A109773 A109774
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KEYWORD
| sign
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com) and Nadia Heninger (nadiah(AT)cs.princeton.edu), Aug 13 2005
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