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A177184 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=-1 and l=-1. 1
1, 9, 15, 107, 479, 3103, 18031, 117727, 755599, 5064687, 34093263, 234114735, 1620229839, 11340760367, 79951746767, 567945479727, 4058390653647, 29163273207087, 210568996777167, 1527068200329007, 11117641676731087 (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=-1, l=-1).

Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(-17*n+43)*a(n-2) +(95*n-298)*a(n-3) +4*(-28*n+113)*a(n-4) +40*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016

EXAMPLE

a(2)=2*1*9-2-1=15. a(3)=2*1*15-2+81-1-1=107.

MAPLE

l:=-1: : k := -1 : 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. A177183.

Sequence in context: A029712 A136353 A136354 * A098146 A124274 A075134

Adjacent sequences:  A177181 A177182 A177183 * A177185 A177186 A177187

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, May 04 2010

STATUS

approved

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Last modified December 6 14:49 EST 2016. Contains 278781 sequences.