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A177127 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)=6, k=0 and l=1.

%I A177127 #5 Mar 02 2016 15:29:58
%S A177127 1,6,13,63,283,1492,8019,45270,261219,1542254,9251023,56269627,
%T A177127 346115245,2149556612,13459568885,84879754663,538612428155,
%U A177127 3436623582022,22034604531623,141897138868677,917376314956897
%N A177127 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)=6, k=0 and l=1.
%F A177127 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 A177127 Conjecture: +(n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-11*n+27)*a(n-2) +32*(n-3)*a(n-3) +16*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Mar 02 2016
%e A177127 a(2)=2*1*6+1=13. a(3)=2*1*13+36+1=63. a(4)=2*1*63+2*6*13+1=283.
%p A177127 l:=1: : k := 0 : m :=6: 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 A177127 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 A177127 Cf. A176609.
%K A177127 easy,nonn
%O A177127 0,2
%A A177127 _Richard Choulet_, May 03 2010