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A176757 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)=5, k=0 and l=-2.

%I A176757 #7 Feb 18 2016 14:31:58
%S A176757 1,5,8,39,156,764,3710,19075,99640,533316,2895978,15948420,88781874,
%T A176757 498980622,2827021998,16129973367,92598274980,534480546320,
%U A176757 3099969839270,18057658897612,105598220332966,619702140284970
%N A176757 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)=5, k=0 and l=-2.
%F A176757 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).
%F A176757 Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-7*n+19)*a(n-2) +6*(6*n-19)*a(n-3) +24*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Feb 18 2016
%e A176757 a(2)=2*1*5-2=8. a(3)=2*1*8+5^2-2=39. a(4)=2*1*39+2*4*8-2=156.
%p A176757 l:=-2: : k := 0 : m:=5: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 A176757 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 A176757 Cf. A176756.
%K A176757 easy,nonn
%O A176757 0,2
%A A176757 _Richard Choulet_, Apr 25 2010