%I A098329
%S A098329 1,1,17,49,481,2081,16241,85457,600769,3489601,23391697,143000177,
%T A098329 938797729,5897385313,38397492017,244866166289,1590355308929,
%U A098329 10231490804353,66456634775441,429898281869489,2795449543782241
%N A098329 Expansion of 1/(1-2x-31x^2)^(1/2).
%C A098329 Central coefficient of (1+x+8x^2)^n. 7th binomial transform of 2^n*LegendreP(n,
               -3) (signed version of A084773).
%C A098329 Also number of paths from (0,0) to (n,0) using steps U=(1,1), H=(1,0) 
               and D=(1,-1), the U steps can have 8 colors. - Nour-Eddine Fahssi 
               (fahssin(AT)yahoo.fr), Mar 31 2008
%D A098329 Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, 
               Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
%F A098329 a(n)=sum{k=0..floor(n/2), binomial(n-k, k)binomial(n, k)8^k}.
%F A098329 E.g.f. : exp(x)BesselI(0, 4sqrt(2)x)
%Y A098329 Cf. A084603.
%Y A098329 Sequence in context: A146706 A120612 A146461 this_sequence A160076 A003124 
               A005570
%Y A098329 Adjacent sequences: A098326 A098327 A098328 this_sequence A098330 A098331 
               A098332
%K A098329 easy,nonn
%O A098329 0,3
%A A098329 Paul Barry (pbarry(AT)wit.ie), Sep 03 2004