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~See A335947 for formulas and references concerning the polynomials.

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

~See A335947 for formulas and references concerning the polynomials.

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.

denom(coeffT(smuBpoln, 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).

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;

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;

Cf. A335948 A335947 (numerators),

allocated for Peter Luschny

denom(coeff(smuBpol(n,x), x, k))

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

0,4

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;

Cf. A335948 (numerators),

allocated

nonn,frac,tabl

Peter Luschny, Jul 01 2020

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allocated for Peter Luschny

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