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A176954 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)=2, k=-1 and l=-1. 1
1, 2, 1, 2, 3, 9, 27, 92, 313, 1083, 3753, 13063, 45581, 159501, 559549, 1967878, 6937267, 24511653, 86797683, 308003549, 1095155727, 3901490015, 13924590847, 49784694997, 178293760747, 639543538859, 2297555097259, 8265957750659 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

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=-1, l=-1).

Conjecture: (n+1)*a(n) +(2-7n)*a(n-1) +(11n-13)*a(n-2) + (11n-46)*a(n-3) +4*(29-7n)*a(n-4) +12(n-5)*a(n-5)=0. - R. J. Mathar, Nov 21 2011

EXAMPLE

a(2)=2*1*2-2-1=1. a(3)=2*1*1-2+2^2-1-1=2. a(4)=2*1*2-2+2*2*1-2-1=3.

MAPLE

l:=-1: : k := -1 : m:=2: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. A176953.

Sequence in context: A120405 A252889 A155004 * A034952 A337549 A306456

Adjacent sequences:  A176951 A176952 A176953 * A176955 A176956 A176957

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Apr 29 2010

STATUS

approved

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Last modified April 14 12:11 EDT 2021. Contains 342949 sequences. (Running on oeis4.)