A335948 T(n, k) = denominator([x^k] b_n(x)), where b_n(x) = Sum_{k=0..n} binomial(n,k)* Bernoulli(k, 1/2)*x^(n-k). Triangle read by rows, for n >= 0 and 0 <= k <= n.

1, 1, 1, 12, 1, 1, 1, 4, 1, 1, 240, 1, 2, 1, 1, 1, 48, 1, 6, 1, 1, 1344, 1, 16, 1, 4, 1, 1, 1, 192, 1, 48, 1, 4, 1, 1, 3840, 1, 48, 1, 24, 1, 3, 1, 1, 1, 1280, 1, 16, 1, 40, 1, 1, 1, 1, 33792, 1, 256, 1, 32, 1, 8, 1, 4, 1, 1, 1, 3072, 1, 256, 1, 32, 1, 8, 1, 12, 1, 1

Offset

0,4

Comments

See A335947 for formulas and references concerning the polynomials.

Links

Table of n, a(n) for n=0..77.

Example

First few polynomials are:
b_0(x) = 1;
b_1(x) = x;
b_2(x) = -(1/12) + x^2;
b_3(x) = -(1/4)*x + x^3;
b_4(x) = (7/240) - (1/2)*x^2 + x^4;
b_5(x) = (7/48)*x - (5/6)*x^3 + x^5;
b_6(x) = -(31/1344) + (7/16)*x^2 - (5/4)*x^4 + x^6;
Triangle starts:
1;
1,     1;
12,    1,    1;
1,     4,    1,   1;
240,   1,    2,   1,  1;
1,     48,   1,   6,  1,  1;
1344,  1,    16,  1,  4,  1,  1;
1,     192,  1,   48, 1,  4,  1, 1;
3840,  1,    48,  1,  24, 1,  3, 1, 1;
1,     1280, 1,   16, 1,  40, 1, 1, 1, 1;
33792, 1,    256, 1,  32, 1,  8, 1, 4, 1, 1;

Crossrefs

Cf. A335947 (numerators), A157780 (column 0), A033469 (column 0 even indices only).

Sequence in context: A306682 A327154 A334731 * A010209 A058306 A010207

Adjacent sequences: A335945 A335946 A335947 * A335949 A335950 A335951

Keyword

nonn,frac,tabl

Author

Peter Luschny, Jul 01 2020

Status

approved