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A176610
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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)=0, k=1 and l=1.
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0
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1, 0, 3, 10, 25, 65, 197, 652, 2203, 7523, 26159, 92663, 332747, 1206641, 4411883, 16252550, 60270497, 224798517, 842706069, 3173330573, 11998214633, 45531318219, 173359346313, 662062569685, 2535444644053, 9734529981735
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OFFSET
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0,3
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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=1, l=1).
Conjecture: (n+1)*a(n) +(2-7n)*a(n-1) +(19n-29)*a(n-2) +(110-37n)*a(n-3) +36*(n-4)*a(n-4) +12*(5-n)*a(n-5)=0. - R. J. Mathar, Nov 17 2011
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EXAMPLE
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a(2)=(1*0+1)+(1*0+1)+1=3. a(3)=2*1*3+2+(0^2+1)+1=10. a(4)=2*1*10+2+2*0*3+2+1=25.
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MAPLE
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l:=1: : k := 1 : m:=0: d(0):=1:d(1):=m: for n from 1 to 32 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, 34); seq(d(n), n=0..32);
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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