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A115149
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Tenth convolution of A115140.
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9
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1, -10, 35, -50, 25, -2, 0, 0, 0, 0, -1, -10, -65, -350, -1700, -7752, -33915, -144210, -600875, -2466750, -10015005, -40320150, -161280600, -641886000, -2544619500, -10056336264, -39645171810, -155989499540, -612815891050, -2404551645100, -9425842448792
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OFFSET
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0,2
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COMMENTS
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Because (x*c(x))^n + (1/c(x))^n = L(n,-x)= sum(A034807(n,k)*(-x)^k,k=0..floor(n/2)) the sequence starts with the Lucas polynomial L(10,-x) (of degree 5).
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LINKS
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Table of n, a(n) for n=0..30.
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FORMULA
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O.g.f.: 1/c(x)^10 = P(11, x) - x*P(10, 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(11, x)=1-9*x+28*x^2-35*x^3+15*x^4-x^5 and P(10, x)=1-8*x+21*x^2-20*x^3+5*x^4.
a(n)=-C10(n-10), n>=10, with C10(n):= (n+4) (eighth convolution of Catalan numbers). a(0)=1, a(1)=-10, a(2)=35, a(3)=-50, a(4)=25, a(5)=-2, a(6)=a(7)=a(8)=a(9)=0. [1, -10, 35, -50, 25, -2] is row n=10 of signed A034807 (signed Lucas polynomials).
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CROSSREFS
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Cf. A115148 (ninth convolution).
Sequence in context: A219591 A010818 A065195 * A044087 A022702 A044468
Adjacent sequences: A115146 A115147 A115148 * A115150 A115151 A115152
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KEYWORD
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sign,easy
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AUTHOR
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Wolfdieter Lang, Jan 13 2006
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STATUS
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approved
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