A177170 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=0 and l=-2.
1, 8, 14, 90, 402, 2438, 13826, 86014, 533866, 3431526, 22262130, 146919390, 978782298, 6589079958, 44700139650, 305468697294, 2100216474090, 14519814200198, 100868678209298, 703796972768062, 4929877163487610
Offset: 0
Examples
a(2)=2*1*8-2=14. a(3)=2*1*14+64-2=90.
Crossrefs
Cf. A177169.
Programs
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Maple
l:=-2: : k := 0 : 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 : 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);
Formula
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).
Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-19*n+43)*a(n-2) +6*(10*n-31)*a(n-3) +36*(-n+4)*a(n-4)=0. - R. J. Mathar, Jun 14 2016