A370703 - OEIS

%I #7 Jun 17 2024 15:17:34

%S 1,1,1,1,1,1,1,4,1,1,1,1,1,1,1,1,16,1,2,1,1,1,1,1,1,1,1,1,1,64,1,16,1,

%T 4,1,1,1,1,1,1,1,1,1,1,1,1,256,1,16,1,8,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,

%U 1,1024,1,256,1,32,1,8,1,4,1,1

%N Triangle read by rows: T(n, k) = denominator([x^k] n! [t^n] (t/2 + sqrt(1 + (t/2)^2))^(2*x)).

%e Triangle starts:

%e [0] 1;

%e [1] 1,   1;

%e [2] 1,   1, 1;

%e [3] 1,   4, 1,  1;

%e [4] 1,   1, 1,  1, 1;

%e [5] 1,  16, 1,  2, 1, 1;

%e [6] 1,   1, 1,  1, 1, 1, 1;

%e [7] 1,  64, 1, 16, 1, 4, 1, 1;

%e [8] 1,   1, 1,  1, 1, 1, 1, 1, 1;

%e [9] 1, 256, 1, 16, 1, 8, 1, 1, 1, 1;

%p gf := (t/2 + sqrt(1 + (t/2)^2))^(2*x): ser := series(gf, t, 20):

%p ct := n -> n!*coeff(ser, t, n): T := (n, k) -> denom(coeff(ct(n),x,k)):

%p seq(seq(T(n, k), k = 0..n), n = 0..11);

%Y Cf. A370705 (numerators).

%K nonn,tabl,frac

%O 0,8

%A _Peter Luschny_, Mar 02 2024