%I A084601
%S A084601 1,1,5,13,49,161,581,2045,7393,26689,97285,355565,1305745,4808545,
%T A084601 17760965,65753693,243954113,906758785,3375949829,12587460557,
%U A084601 46995614449,175669746209,657370655045,2462383495357,9232029156001
%N A084601 Coefficients of 1/(1-2x-7x^2)^(1/2); also, a(n) is the central coefficient 
               of (1+x+2x^2)^n.
%C A084601 The Hankel transform (see A001906 for definition) of this sequence is 
               A036442 : 1, 4, 32, 512, 16384, ... . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Jul 03 2005
%C A084601 Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) 
               and D=(1,-1), U (or D) can have 2 colors. - Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), 
               Feb 05 2008
%D A084601 Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, 
               Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
%F A084601 E.g.f.: exp(x)*BesselI(0, 2*sqrt(2)*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Mar 21 2004
%F A084601 a(n)=sum{k=0..floor(n/2), binomial(n-k, k)binomial(n, k)2^k}. - Paul 
               Barry (pbarry(AT)wit.ie), Aug 26 2004
%F A084601 Sum[k=0..n, Trinomial(k, n) Binomial(n, k) ], with Trinomial=A027907. 
               - R. Stephan, Jan 28 2005
%F A084601 a(n) is also the central coefficient of (2+x+x^2)^n; a(n)=sum_{k=0..n} 
               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), Feb 05 2008
%o A084601 (PARI) for(n=0,30,t=polcoeff((1+x+2*x^2)^n,n,x); print1(t","))
%Y A084601 Cf. A002426, A084600, A084602-A084615.
%Y A084601 Sequence in context: A146152 A082132 A138277 this_sequence A149532 A149533 
               A149534
%Y A084601 Adjacent sequences: A084598 A084599 A084600 this_sequence A084602 A084603 
               A084604
%K A084601 nonn
%O A084601 0,3
%A A084601 Paul D. Hanna (pauldhanna(AT)juno.com), Jun 01 2003