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A115148
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Ninth convolution of A115140.
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1
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1, -9, 27, -30, 9, 0, 0, 0, 0, -1, -9, -54, -273, -1260, -5508, -23256, -95931, -389367, -1562275, -6216210, -24582285, -96768360, -379629720, -1485507600, -5801732460, -22626756594, -88152205554, -343176898988, -1335293573130, -5193831553416
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| O.g.f.: 1/c(x)^9 = P(10, x) - x*P(9, x)*c(x) with the o.g.f. c(x):=(1-sqrt(1-4*x))/(2*x) of A000108 (Catalan numbers) and the polynomials P(n, x) defined in A115139. Here P(10, x)=1-8*x+21*x^2-20*x^3+5*x^4 and P(9, x)=1-7*x+15*x^2-10*x^3+x^4.
a(n)=-C9(n-9), n>=9, with C9(n):=A001392(n+4) (eighth convolution of Catalan numbers). a(0)=1, a(1)=-9, a(2)=27, a(3)=-30, a(4)=9, a(5)=a(6)=a(7)=a(8)=0. [1, -9, 27, -30, 9] is row n=9 of signed A034807 (signed Lucas polynomials). See A115149 and A034807 for comments.
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CROSSREFS
| Cf. A115147 (eighth convolution).
Sequence in context: A010817 A205973 A122985 * A022701 A108107 A036303
Adjacent sequences: A115145 A115146 A115147 * A115149 A115150 A115151
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KEYWORD
| sign,easy
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jan 13 2006
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