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A335948
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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.
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2
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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
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OFFSET
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0,4
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COMMENTS
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See A335947 for formulas and references concerning the polynomials.
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LINKS
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Table of n, a(n) for n=0..77.
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EXAMPLE
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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;
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CROSSREFS
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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
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KEYWORD
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nonn,frac,tabl
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AUTHOR
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Peter Luschny, Jul 01 2020
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STATUS
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approved
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