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 A177167 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)=10, k=0 and l=-1. 0
 1, 10, 19, 137, 653, 4406, 27077, 185856, 1259601, 8898900, 63225681, 457994141, 3345121235, 24706965674, 183830383235, 1378149812989, 10393740091309, 78828658428280, 600737927801161, 4598286755156991, 35334943369372359 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS FORMULA 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=-1). Conjecture: (n+1)*a(n) +2(1-3n)*a(n-1) +(59-27n)*a(n-2) +4(18n-55)*a(n-3) +40(4-n)*a(n-4)=0. - R. J. Mathar, Nov 27 2011 EXAMPLE a(2)=2*1*10-1=19. a(3)=2*1*19+100-1=137. MAPLE l:=-1: : k := 0 : for m from 0 to 10 do 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): od; CROSSREFS Sequence in context: A220005 A253213 A177203 * A073222 A110463 A121725 Adjacent sequences:  A177164 A177165 A177166 * A177168 A177169 A177170 KEYWORD easy,nonn AUTHOR Richard Choulet, May 04 2010 STATUS approved

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