cp's OEIS Frontend

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.

%I A197420 #8 Dec 13 2013 03:14:39
%S A197420 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,
%T A197420 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,
%U A197420 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
%N 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.
%C A197420 Denominators of the polynomials defined in A197419.
%H A197420 R. Dere, Y. Simsek, <a href="http://arxiv.org/abs/1110.1484">Bernoulli type polynomials on Umbral Algebra</a>, arXiv:1110.1484 [math.CA]
%e A197420 1;
%e A197420 1,1;
%e A197420 6,1,1;
%e A197420 2,2,1,1;
%e A197420 10,1,1,1,1;
%e A197420 6,2,1,3,1,1;
%e A197420 42,1,2,1,2,1,1;
%e A197420 6,6,2,2,2,2,1,1;
%e A197420 30,3,3,3,1,1,3,1,1;
%e A197420 10,10,1,1,1,5,1,1,1,1;
%e A197420 22,1,2,1,1,1,1,1,2,1,1;
%e A197420 6,2,2,2,1,1,1,1,2,6,1,1;
%e A197420 2730,1,1,1,2,1,1,1,2,1,1,1,1;
%t A197420 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_ *)
%K A197420 nonn,tabl,frac
%O A197420 0,4
%A A197420 _R. J. Mathar_, Oct 14 2011