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%I #21 Jan 29 2023 15:05:23
%S 1,5,40,395,4360,51530,637840,8163095,107140360,1434252230,
%T 19507077040,268796321870,3744480010960,52647783144980,
%U 746145741252640,10648007952942095,152877753577617160,2206713692628578030
%N a(n) = Sum_{k=0..n} C(n+k,2k)*A000108(k)*3^k*2^(n-k).
%C Hankel transform is 15^C(n+1,2).
%F a(n) = A152600(n+1)/2.
%F a(n) = Sum_{k=0..n} A088617(n,k)*3^k*2^(n-k) = Sum_{k=0..n} A060693(n,k)*2^k*3^(n-k). - _Philippe Deléham_, Dec 10 2008
%F a(n) = Sum_{k=0..n} A090181(n,k)*5^k*3^(n-k). - _Philippe Deléham_, Dec 10 2008
%F a(n) = Sum_{k=0..n} A131198(n,k)*3^k*5^(n-k). - _Philippe Deléham_, Dec 10 2008
%F a(n) = Sum_{k=0..n} A133336(n,k)*(-2)^k*5^(n-k) = Sum_{k=0..n} A086810(n,k)*5^k*(-2)^(n-k). - _Philippe Deléham_, Dec 10 2008
%F G.f.: 1/(1-5x/(1-3x/(1-5x/(1-3x/(1-5x/(1-3x/(1-5x/(1-... (continued fraction). - _Philippe Deléham_, Nov 28 2011
%F Conjecture: (n+1)*a(n) +8*(-2*n+1)*a(n-1) +4*(n-2)*a(n-2)=0. - _R. J. Mathar_, Nov 24 2012
%F G.f.: 1/G(x), with G(x) = 1-2*x-(3*x)/G(x) (continued fraction). - _Nikolaos Pantelidis_, Jan 09 2023
%Y Cf. A103211, A103210.
%Y Cf. A088617, A060693, A090181, A131198, A133336, A086810
%Y Cf. A152600.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Dec 09 2008
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