cp's OEIS Frontend

A370703 Triangle read by rows: T(n, k) = denominator([x^k] n! [t^n] (t/2 + sqrt(1 + (t/2)^2))^(2*x)).

%I A370703 #7 Jun 17 2024 15:17:34
%S A370703 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 A370703 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 A370703 1,1024,1,256,1,32,1,8,1,4,1,1
%N A370703 Triangle read by rows: T(n, k) = denominator([x^k] n! [t^n] (t/2 + sqrt(1 + (t/2)^2))^(2*x)).
%e A370703 Triangle starts:
%e A370703 [0] 1;
%e A370703 [1] 1,   1;
%e A370703 [2] 1,   1, 1;
%e A370703 [3] 1,   4, 1,  1;
%e A370703 [4] 1,   1, 1,  1, 1;
%e A370703 [5] 1,  16, 1,  2, 1, 1;
%e A370703 [6] 1,   1, 1,  1, 1, 1, 1;
%e A370703 [7] 1,  64, 1, 16, 1, 4, 1, 1;
%e A370703 [8] 1,   1, 1,  1, 1, 1, 1, 1, 1;
%e A370703 [9] 1, 256, 1, 16, 1, 8, 1, 1, 1, 1;
%p A370703 gf := (t/2 + sqrt(1 + (t/2)^2))^(2*x): ser := series(gf, t, 20):
%p A370703 ct := n -> n!*coeff(ser, t, n): T := (n, k) -> denom(coeff(ct(n),x,k)):
%p A370703 seq(seq(T(n, k), k = 0..n), n = 0..11);
%Y A370703 Cf. A370705 (numerators).
%K A370703 nonn,tabl,frac
%O A370703 0,8
%A A370703 _Peter Luschny_, Mar 02 2024