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A177179
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, 19, 121, 587, 3717, 22603, 149065, 988291, 6762757, 46812915, 329336265, 2340489211, 16803807621, 121604988955, 886446236169, 6501729726195, 47952147336325, 355387114288451, 2645435985621257, 19769671436457963
OFFSET
0,2
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) +(79*n-242)*a(n-3) +4*(-22*n+89)*a(n-4) +32*(n-5)*a(n-5)=0. - R. J. Mathar, Mar 02 2016
EXAMPLE
a(2)=2*1*9+2-1=19. a(3)=2*1*19+2+81+1-1=121.
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. A177178.
Sequence in context: A165247 A177130 A240120 * A335782 A041677 A153316
KEYWORD
easy,nonn
AUTHOR
Richard Choulet, May 04 2010
STATUS
approved