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A177171 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. 1
1, 9, 16, 111, 508, 3268, 19230, 125859, 815208, 5494796, 37280170, 257711524, 1796835778, 12665947790, 89949355454, 643580501287, 4632487753748, 33531130466872, 243877573413062, 1781555056684620, 13065400778105878 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

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=-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

EXAMPLE

a(2)=2*1*9-2=16. a(3)=2*1*16+81-2=111.

MAPLE

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);

CROSSREFS

Cf. A177170.

Sequence in context: A179307 A014720 A138238 * A226232 A267088 A204268

Adjacent sequences:  A177168 A177169 A177170 * A177172 A177173 A177174

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, May 04 2010

STATUS

approved

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Last modified January 20 08:54 EST 2022. Contains 350471 sequences. (Running on oeis4.)