A356653 Triangle read by rows. Denominators of the coefficients of a sequence of rational polynomials r_n(x) with r_n(1) = B(2*n), where B(n) are the Bernoulli numbers.

1, 1, 6, 1, 70, 21, 1, 434, 31, 93, 1, 2286, 1905, 127, 1143, 1, 11242, 1533, 511, 73, 219, 1, 53222, 14329, 10235, 2047, 2047, 6141, 1, 245730, 40955, 40955, 368595, 24573, 8191, 73719, 1, 1114078, 294903, 4681, 491505, 42129, 4681, 14043, 42129

Offset: 0

Author

Peter Luschny, Sep 02 2022

Keywords

• nonn
• frac
• tabl

Comments

For formulas and comments see A356652.

Examples

			The triangle T(n, k) begins:
[0] 1;
[1] 1,     6;
[2] 1,    70,    21;
[3] 1,   434,    31,    93;
[4] 1,  2286,  1905,   127, 1143;
[5] 1, 11242,  1533,   511,   73,  219;
[6] 1, 53222, 14329, 10235, 2047, 2047, 6141;
		

Crossrefs

Cf. A356652 (numerators), A269941.

Programs

Maple

# Using function PTrans from A269941.
R_row := n -> seq(coeffs(p), p in PTrans(n, n -> 1/((2*n)*(2*n + 1)),
n -> (2*n)!/(2-2^(2*n)))): seq(lprint(seq(denom(r), r in R_row(n))), n=0..9);

Formula

T(n, k) = denominator([x^k] r_n(x)), where the polynomials r_n(x) are defined in A356652.