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Search: id:A115143
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| 1, -4, 2, 0, -1, -4, -14, -48, -165, -572, -2002, -7072, -25194, -90440, -326876, -1188640, -4345965, -15967980, -58929450, -218349120, -811985790, -3029594040, -11338026180, -42550029600, -160094486370, -603784920024, -2282138106804, -8643460269248, -32798844771700
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OFFSET
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0,2
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FORMULA
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O.g.f.: 1/c(x)^4 = P(5, x) - x*P(4, 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(5, x)=1-5*x+6*x^2-x^3 and P(4, x)=1-2*x.
a(n)=-C4(n-4), n>=4, with C4(n):=A002057(n) (fourth convolution of Catalan numbers). a(0)=1, a(1)=-4, a(2)=2, a(3)=0. [1, -4, 2] is row n=4 of signed A034807 (signed Lucas polynomials). See A115149 and A034807 for comments.
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CROSSREFS
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Cf. A115142 (third convolution).
Sequence in context: A107088 A137986 A093486 this_sequence A093556 A021242 A088393
Adjacent sequences: A115140 A115141 A115142 this_sequence A115144 A115145 A115146
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KEYWORD
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sign,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Jan 13 2006
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