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%I #25 Jan 30 2020 21:29:14
%S 1,5,30,185,1150,7170,44760,279585,1746870,10916150,68219860,
%T 426353130,2664633580,16653699860,104084695500,650526003825,
%U 4065775405350,25411052086350,158818913483700,992617612224750,6203857867325700,38774103465635100,242338116077385600
%N G.f.: 1/(1 - 5*x*C(x)), where C(x) = (1 - sqrt(1 - 4*x))/(2*x) = g.f. for the Catalan numbers A000108.
%C Numbers have the same parity as the Catalan numbers, that is, a(n) is even except for n of the form 2^m - 1. Follows from C(x) = 1/(1 - x*C(x)) = 1/(1 - 5*x*C(x)) (mod 2). - _Peter Bala_, Jul 24 2016
%F a(n) = Sum_{k = 0..n} A106566(n, k)*5^k. - _Philippe Deléham_, Sep 01 2005
%F a(n) = Sum{k = 0..n} A039599(n,k)*4^k. - _Philippe Deléham_, Sep 08 2007
%F a(0) = 1, a(n) = (25*a(n-1) - 5*A000108(n-1))/4 for n >= 1. - _Philippe Deléham_, Nov 27 2007
%F a(n) = Sum_{k = 0..n} A116395(n,k)*3^k. - _Philippe Deléham_, Sep 27 2009
%F D-finite with recurrence: +4*n*a(n) +(-41*n+24)*a(n-1) +50*(2*n-3)*a(n-2)=0. - _R. J. Mathar_, Jan 20 2020
%F a(n) = 5*A076025(n), n>0. - _R. J. Mathar_, Jan 20 2020
%o (PARI) C(x) = (1 - sqrt(1 - 4*x))/(2*x);
%o my(x = 'x + O('x^25)); Vec(1/(1 - 5*x*C(x))) \\ _Michel Marcus_, Jan 21 2020
%Y Cf. A000108, A000984, A007854, A076035, A126694.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Oct 29 2002
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