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A177131 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)=10, k=0 and l=1.

%I A177131 #5 Jan 20 2014 22:19:36
%S A177131 1,10,21,143,707,4716,29579,203622,1399099,9961582,71585287,523465627,
%T A177131 3864076389,28826865756,216722056701,1641392860951,12507535829603,
%U A177131 95839985593950,737953189846751,5707113130311621,44310704176742745
%N A177131 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)=10, k=0 and l=1.
%F A177131 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 A177131 Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-27*n+59)*a(n-2) +64*(n-3)*a(n-3) +32*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Jul 24 2012
%e A177131 a(2)=2*1*10+1=21. a(3)=2*1*21+100+1=143.
%p A177131 l:=1: : k := 0 : m :=10: 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 A177131 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 A177131 Cf. A177130.
%K A177131 easy,nonn
%O A177131 0,2
%A A177131 _Richard Choulet_, May 03 2010