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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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Denominators of the polynomials defined in A197419.

LINKS

Table of n, a(n) for n=0..90.

R. Dere, Y. Simsek, Bernoulli type polynomials on Umbral Algebra, arXiv:1110.1484 [math.CA]

EXAMPLE

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;

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-Fran├žois Alcover, Dec 12 2013, after Vladimir Kruchinin *)

CROSSREFS

Sequence in context: A316623 A108131 A073354 * A128423 A345628 A336179

Adjacent sequences:  A197417 A197418 A197419 * A197421 A197422 A197423

KEYWORD

nonn,tabl,frac

AUTHOR

R. J. Mathar, Oct 14 2011

STATUS

approved

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Last modified October 26 11:10 EDT 2021. Contains 348267 sequences. (Running on oeis4.)