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A177128 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)=7, k=0 and l=1.

%I A177128 #5 Mar 02 2016 15:59:18
%S A177128 1,7,15,80,371,2088,11771,70305,427405,2663932,16853341,108166507,
%T A177128 701904555,4599254190,30383303055,202154463130,1353408327935,
%U A177128 9110887281150,61632613465475,418751976874065,2856336340630845
%N A177128 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)=7, k=0 and l=1.
%F A177128 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=1).
%F A177128 Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +5*(-3*n+7)*a(n-2) +40*(n-3)*a(n-3) +20*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Mar 02 2016
%e A177128 a(2)=2*1*7+1=15. a(3)=2*1*15+7^2+1=80.
%p A177128 l:=1: : k := 0 : m :=7: d(0):=1:d(1):=m: for n from 1 to 28 do d(n+1):=sum(d(p)*d(n-p)+k, p=0..n)+l:od :
%p A177128 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, 31); seq(d(n), n=0..29);
%Y A177128 Cf. A177127.
%K A177128 easy,nonn
%O A177128 0,2
%A A177128 _Richard Choulet_, May 03 2010