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

0,3

Comments

For formulas and comments see A356652.

Links

Table of n, a(n) for n=0..44.

Formula

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

Example

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;

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);

Crossrefs

Cf. A356652 (numerators), A269941.

Sequence in context: A134278 A049385 A266364 * A009384 A280520 A051151

Adjacent sequences: A356650 A356651 A356652 * A356654 A356655 A356656

Keyword

nonn,frac,tabl

Author

Peter Luschny, Sep 02 2022

Status

approved