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A176756
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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)=4, k=0 and l=-2.
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1
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1, 4, 6, 26, 98, 438, 1970, 9294, 44698, 219766, 1096930, 5549614, 28383498, 146538150, 762627954, 3996744862, 21074272538, 111723476502, 595145562242, 3183988894350, 17100312159018, 92164073738118, 498318304290450
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OFFSET
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0,2
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LINKS
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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=0, l=-2).
Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-3*n+11)*a(n-2) +2*(14*n-45)*a(n-3) +20*(-n+4)*a(n-4)=0. - R. J. Mathar, Feb 18 2016
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EXAMPLE
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a(2)=2*1*4-2=6. a(3)=2*1*6+4^2-2=26. a(4)=2*1*26+2*4*6-2=98.
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MAPLE
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l:=-2: : k := 0 : m:=4: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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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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