%I A091885
%S A091885 1,1,1,1,4,1,9,10,1,64,20,1,225,259,35,1,2304,784,56,1,11025,12916,1974,
%T A091885 84,1,147456,52480,4368,120,1,893025,1057221,172810,8778,165,1,14745600,
%U A091885 5395456,489280,16368,220,1,108056025,128816766,21967231,1234948,28743
%N A091885 Triangle T(n,k) defined by the generating function (in Maple notation): 
               cosh(sqrt(y)*arcsin(x)) + sqrt(y)*sinh(sqrt(y)*arcsin(x))-1 = sum(sum(T(n,
               k)*y^k, k = 1..n)*x^n/n!, n = 1..infinity).
%C A091885 Row sums are equal to A006228(n). This is sequence A121408 without the 
               intertwining zeros. - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Jul 28 2006
%e A091885 Triangle starts:
%e A091885 1;
%e A091885 1;
%e A091885 1,1;
%e A091885 4,1;
%e A091885 9,10,1;
%e A091885 64,20,1;
%e A091885 225,259,35,1;
%p A091885 G:=cosh(sqrt(y)*arcsin(x))+sqrt(y)*sinh(sqrt(y)*arcsin(x))-1: Gser:=simplify(series(G,
               x=0,15)): for n from 1 to 13 do P[n]:=sort(expand(n!*coeff(Gser,x,
               n))) od: for n from 1 to 13 do seq(coeff(P[n],y,k),k=1..ceil(n/2)) 
               od; # yields sequence in triangular form - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Jul 28 2006
%Y A091885 Cf. A006228.
%Y A091885 Cf. A121408.
%Y A091885 Sequence in context: A084887 A067015 A158199 this_sequence A069606 A001254 
               A075150
%Y A091885 Adjacent sequences: A091882 A091883 A091884 this_sequence A091886 A091887 
               A091888
%K A091885 nonn,tabf,easy
%O A091885 1,5
%A A091885 Karol A. Penson (penson(AT)lptl.jussieu.fr), Feb 08 2004
%E A091885 More terms from Pab Ter (pabrlos(AT)yahoo.com), May 25 2004