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A176958
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Sequence defined by the recurrence formula a(n+1)=sum(a(p)*a(n-p)+k,p=0..n)+l for n>=1, with here a(0)=1, a(1)=5, k=-1 and l=-1.
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1
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1, 5, 7, 35, 135, 663, 3159, 16055, 82423, 434247, 2317623, 12547975, 68644919, 379136007, 2110601527, 11832031495, 66734423095, 378429810183, 2156265145143, 12339184691207, 70884648719415, 408640406413319
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OFFSET
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0,2
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LINKS
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Table of n, a(n) for n=0..21.
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FORMULA
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G.f f: f(z)=(1-sqrt(1-4*z*(a(0)-z*a(0)^2+z*a(1)+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z) (k=-1, l=-1).
Conjecture: (n+1)*a(n) +(-7*n+2)*a(n-1) +(-n+11)*a(n-2) +(47*n-154)*a(n-3) +4*(-16*n+65)*a(n-4) +24*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016
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EXAMPLE
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a(2)=2*1*5-2-1=7. a(3)=2*1*7-2+5^2-1-1=35. a(4)=2*1*35-2+2*5*7-2-1=135.
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MAPLE
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l:=-1: : k := -1 : m:=5:d(0):=1:d(1):=m: for n from 1 to 30 do d(n+1):=sum(d(p)*d(n-p)+k, p=0..n)+l:od :
taylor((1-sqrt(1-4*z*(d(0)-z*d(0)^2+z*m+(k+l)*z^2/(1-z)+k*z^2/(1-z)^2)))/(2*z), z=0, 30); seq(d(n), n=0..30);
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CROSSREFS
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Cf. A176957.
Sequence in context: A175667 A341063 A018353 * A196203 A196473 A081851
Adjacent sequences: A176955 A176956 A176957 * A176959 A176960 A176961
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KEYWORD
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easy,nonn
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AUTHOR
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Richard Choulet, Apr 29 2010
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STATUS
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approved
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