A197420 Triangle with the denominator of the coefficient [x^k] of the second order Bernoulli polynomial B_n^(2)(x) in row n, column 0<=k<=n.
1, 1, 1, 6, 1, 1, 2, 2, 1, 1, 10, 1, 1, 1, 1, 6, 2, 1, 3, 1, 1, 42, 1, 2, 1, 2, 1, 1, 6, 6, 2, 2, 2, 2, 1, 1, 30, 3, 3, 3, 1, 1, 3, 1, 1, 10, 10, 1, 1, 1, 5, 1, 1, 1, 1, 22, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 6, 2, 2, 2, 1, 1, 1, 1, 2, 6, 1, 1, 2730, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1
Offset: 0
Examples
1; 1,1; 6,1,1; 2,2,1,1; 10,1,1,1,1; 6,2,1,3,1,1; 42,1,2,1,2,1,1; 6,6,2,2,2,2,1,1; 30,3,3,3,1,1,3,1,1; 10,10,1,1,1,5,1,1,1,1; 22,1,2,1,1,1,1,1,2,1,1; 6,2,2,2,1,1,1,1,2,6,1,1; 2730,1,1,1,2,1,1,1,2,1,1,1,1;
Links
- R. Dere, Y. Simsek, Bernoulli type polynomials on Umbral Algebra, arXiv:1110.1484 [math.CA]
Programs
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Mathematica
t[n_, m_] := If [n == m, 1, 2*Binomial[n, m]*Sum[StirlingS2[n-m, k]*StirlingS1[2+k, 2]/((k+1)*(2+k)), {k, 1, n-m}]]; Table[t[n, m] // Denominator, {n, 0, 12}, {m, 0, n}] // Flatten (* Jean-François Alcover, Dec 12 2013, after Vladimir Kruchinin *)
Comments