%I A084605
%S A084605 1,1,9,25,145,561,2841,12489,60705,281185,1353769,6418809,30917041,
%T A084605 148331665,716698425,3462260265,16786700865,81464917185,396215601225,
%U A084605 1929237099225,9408084660945,45928695279345,224476389327705
%N A084605 G.f.: 1/(1-2x-15x^2)^(1/2); also, a(n) is the central coefficient of 
               (1+x+4x^2)^n.
%C A084605 Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) 
               and D=(1,-1), the U (or D) steps come in four colors. - Nour-Eddine 
               Fahssi (fahssin(AT)yahoo.fr), Mar 30 2008
%D A084605 Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, 
               Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
%F A084605 E.g.f.: exp(x)*BesselI(0, 4*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Aug 20 2003
%F A084605 a(n) is also the central coefficient of (4+x+x^2)^n; a(n)=sum_{k=0..n} 
               3^(n-k) C(n,k) T(k,n), where T(k,n) is the triangle of trinomial 
               coefficients = Coefficient of x^n of (1+x+x^2)^k : A027907 - Nour-Eddine 
               Fahssi (fahssin(AT)yahoo.fr), Mar 30 2008
%o A084605 (PARI) for(n=0,30,t=polcoeff((1+x+4*x^2)^n,n,x); print1(t","))
%Y A084605 Cf. A002426, A084600-A084604, A084606-A084615.
%Y A084605 Sequence in context: A139818 A146365 A146373 this_sequence A098773 A089998 
               A014728
%Y A084605 Adjacent sequences: A084602 A084603 A084604 this_sequence A084606 A084607 
               A084608
%K A084605 nonn
%O A084605 0,3
%A A084605 Paul D. Hanna (pauldhanna(AT)juno.com), Jun 01 2003