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A177183 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)=8, k=-1 and l=-1. 1

%I #5 Mar 02 2016 15:57:23

%S 1,8,13,86,375,2289,12807,79376,487669,3112659,20011341,131002051,

%T 865156193,5775171729,38841026305,263161175842,1793749636759,

%U 12294401226021,84671929129311,585688412266001,4067110924673259

%N 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)=8, k=-1 and l=-1.

%F 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).

%F Conjecture: +(n+1)*a(n) +(-7*n+2)*a(n-1) +(-13*n+35)*a(n-2) +(83*n-262)*a(n-3) +4*(-25*n+101)*a(n-4) +36*(n-5)*a(n-5)=0. - _R. J. Mathar_, Mar 02 2016

%e a(2)=2*1*8-2-1=13. a(3)=2*1*13-2+64-1-1=86.

%p l:=-1: : k := -1 : m:=8: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 :

%p 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);

%Y Cf. A177182.

%K easy,nonn

%O 0,2

%A _Richard Choulet_, May 04 2010

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)