This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A176750 #5 Feb 18 2016 14:13:50 %S A176750 1,4,7,29,113,506,2321,11112,54429,272364,1384701,7135397,37178543, %T A176750 195556526,1036967927,5537451445,29752654081,160731437308, %U A176750 872518135861,4756932856431,26035840213731,143003903810742,787983925181427 %N A176750 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)=4, k=0 and l=-1. %F A176750 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 A176750 Conjecture: (n+1)*a(n) +2*(-3*n+1)*a(n-1) +(-3*n+11)*a(n-2) +4*(6*n-19)*a(n-3) +16*(-n+4)*a(n-4)=0. - _R. J. Mathar_, Feb 18 2016 %e A176750 a(2)=2*1*4-1=7. a(3)=2*1*7+4^2-1=29. a(4)=2*1*29+2*4*7-1=113. %p A176750 l:=-1: : k := 0 : m:=4: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); %Y A176750 Cf. A176749. %K A176750 easy,nonn %O A176750 0,2 %A A176750 _Richard Choulet_, Apr 25 2010