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%I #5 Jul 16 2019 10:33:23
%S 1,1,1,3,1,1,3,4,1,1,10,4,5,1,1,10,15,5,6,1,1,35,15,21,6,7,1,1,35,56,
%T 21,28,7,8,1,1,126,56,84,28,36,8,9,1,1,126,210,84,120,36,45,9,10,1,1,
%U 462,210,330,120,165,45,55,10,11,1,1
%N Riordan array ((1+x)c(x^2)/sqrt(1-4x^2),xc(x^2)), c(x) the g.f. of A000108.
%C Row sums are A117186. Diagonal sums are A117187. Inverse is A117185.
%F Number triangle T(n,k)=C(n+1,(n+k)/2+1)(1+(-1)^(n-k))/2+C(n,(n+k)/2+1/2)(1-(-1)^(n-k))/2; Column k has e.g.f. Bessel_I(k,2x)+Bessel_I(k+1,2x)+Bessel_I(k+2,2x).
%e Triangle begins
%e 1,
%e 1, 1,
%e 3, 1, 1,
%e 3, 4, 1, 1,
%e 10, 4, 5, 1, 1,
%e 10, 15, 5, 6, 1, 1,
%e 35, 15, 21, 6, 7, 1, 1,
%e 35, 56, 21, 28, 7, 8, 1, 1
%t c[x_] := (1 - Sqrt[1 - 4 x])/(2 x);
%t (* The function RiordanArray is defined in A256893. *)
%t RiordanArray[(1 + #) c[#^2]/Sqrt[1 - 4 #^2]&, # c[#^2]&, 11] // Flatten (* _Jean-François Alcover_, Jul 16 2019 *)
%K easy,nonn,tabl
%O 0,4
%A _Paul Barry_, Mar 01 2006
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