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%I #22 Jan 09 2023 09:31:59
%S 1,6,6,42,114,654,2526,13506,61242,321558,1579830,8311578,42655938,
%T 226373406,1192341390,6391471794,34239385482,185275416102,
%U 1004459653734,5480384744202,29980061984274,164732303389614,907579024283454
%N a(n) = Sum_{i=0..n-1} a(i)*a(n-i) with a(0)=1, a(1)=6.
%H Vincenzo Librandi, <a href="/A014435/b014435.txt">Table of n, a(n) for n = 0..200</a>
%F G.f.: ( (1+x)-sqrt(1-2*x-23*x^2) ) / (2*x).
%F a(n) ~ sqrt((12-sqrt(6))/23) * (1+2*sqrt(6))^(n+1) / (2*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Feb 09 2014
%F G.f.: 1 + 6*x/G(x) with G(x) = (1 - x - 6*x^2/G(x)) (continued fraction). - _Nikolaos Pantelidis_, Dec 17 2022
%p seq(coeff(convert(series(((1+x)-sqrt(1-2*x-23*x^2))/(2*x),x,40),polynom),x,i),i=0..25); A014435:=proc(n) options remember: local i: if n<2 then RETURN([1,6][n+1]) else RETURN(add(A014435(i)*A014435(n-1-i),i=0..n-2)) fi:end;seq(A014435(n),n=0..25); # (C. Ronaldo)
%t CoefficientList[Series[(1+x-Sqrt[1-2*x-23*x^2])/(2*x), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Feb 09 2014 *)
%K nonn
%O 0,2
%A _Wouter Meeussen_