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

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, 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, 1, 1024, 1, 256, 1, 32, 1, 8, 1, 4, 1, 1

Offset: 0

Author

Peter Luschny, Mar 02 2024

Keywords

• nonn
• tabl
• frac

Examples

			Triangle starts:
[0] 1;
[1] 1,   1;
[2] 1,   1, 1;
[3] 1,   4, 1,  1;
[4] 1,   1, 1,  1, 1;
[5] 1,  16, 1,  2, 1, 1;
[6] 1,   1, 1,  1, 1, 1, 1;
[7] 1,  64, 1, 16, 1, 4, 1, 1;
[8] 1,   1, 1,  1, 1, 1, 1, 1, 1;
[9] 1, 256, 1, 16, 1, 8, 1, 1, 1, 1;
		

Crossrefs

Cf. A370705 (numerators).

Programs

Maple

gf := (t/2 + sqrt(1 + (t/2)^2))^(2*x): ser := series(gf, t, 20):
ct := n -> n!*coeff(ser, t, n): T := (n, k) -> denom(coeff(ct(n),x,k)):
seq(seq(T(n, k), k = 0..n), n = 0..11);