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A045902 Catafusenes (see reference for precise definition).

%I A045902 #17 Mar 08 2020 03:35:15
%S A045902 1,4,18,80,355,1580,7066,31772,143645,652860,2981910,13682328,
%T A045902 63046776,291646860,1353967250,6306552800,29464361530,138045441260,
%U A045902 648449195350,3053348997200,14409512770575,68143962854836,322886537205062,1532716400556220,7288075248828605,34710221395625380
%N A045902 Catafusenes (see reference for precise definition).
%C A045902 4-fold convolution of A002212. Convolution of A045868 with itself. - _Emeric Deutsch_, Mar 13 2004
%D A045902 S. J. Cyvin et al., Enumeration and classification of certain polygonal systems... : annelated catafusenes, J. Chem. Inform. Comput. Sci., 34 (1994), 1174-1180.
%H A045902 Vincenzo Librandi, <a href="/A045902/b045902.txt">Table of n, a(n) for n = 0..200</a>
%F A045902 G.f.: (1 - x - sqrt(1-6*x+5*x^2))^4/(16*x^4). - _Emeric Deutsch_, Mar 13 2004
%F A045902 a(n) = (4/n)*Sum_{j=1..n} binomial(n, j)*binomial(2j+3, j-1) for n >= 1. - _Emeric Deutsch_, Mar 25 2004
%F A045902 Recurrence: (n+1)*(n+4)*a(n) = (6*n^2+19*n+19)*a(n-1) - 5*(n-2)*(n+2)*a(n-2). - _Vaclav Kotesovec_, Oct 08 2012
%F A045902 a(n) ~ 16*5^(n+1/2)/(sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Oct 08 2012
%p A045902 a := n->(4/n)*sum(binomial(n,j)*binomial(2*j+3,j-1),j=1..n): 1,seq(a(n),n=1..22);
%t A045902 Table[SeriesCoefficient[(1-x-Sqrt[1-6*x+5*x^2])^4/(16*x^4),{x,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 08 2012 *)
%o A045902 (PARI) x='x+O('x^66); Vec((1-x-sqrt(1-6*x+5*x^2))^4/(16*x^4)) \\ _Joerg Arndt_, May 04 2013
%Y A045902 Cf. A002212, A045868.
%K A045902 nonn
%O A045902 0,2
%A A045902 _N. J. A. Sloane_
%E A045902 More terms from _Emeric Deutsch_, Mar 13 2004