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A177171
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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)=9, k=0 and l=-2.
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1
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1, 9, 16, 111, 508, 3268, 19230, 125859, 815208, 5494796, 37280170, 257711524, 1796835778, 12665947790, 89949355454, 643580501287, 4632487753748, 33531130466872, 243877573413062, 1781555056684620, 13065400778105878
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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) +(-23*n+51)*a(n-2) +2*(34*n-105)*a(n-3) +40*(-n+4)*a(n-4)=0. - R. J. Mathar, Mar 02 2016
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EXAMPLE
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a(2)=2*1*9-2=16. a(3)=2*1*16+81-2=111.
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MAPLE
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l:=-2: : k := 0 : m:=9: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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