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A276997 Denominators of coefficients of polynomials arising from applying the complete Bell polynomials to k!B_k(x)/(k*(k-1)) with B_k(x) the Bernoulli polynomials.

%I A276997 #17 Sep 09 2018 11:15:33
%S A276997 1,1,1,6,1,1,1,2,2,1,60,1,1,1,1,1,6,2,3,1,1,504,4,4,1,1,1,1,1,24,8,12,
%T A276997 2,2,2,1,2160,18,9,3,2,1,3,1,1,1,60,4,6,1,5,1,1,1,1,3168,48,16,6,3,2,
%U A276997 2,1,2,1,1,1,288,32,144,12,12,4,2,1,6,2,1
%N A276997 Denominators of coefficients of polynomials arising from applying the complete Bell polynomials to k!B_k(x)/(k*(k-1)) with B_k(x) the Bernoulli polynomials.
%C A276997 For formulas and references see A276996.
%C A276997 Compare T(n,0) with A220411.
%e A276997 Triangle starts:
%e A276997      1;
%e A276997      1,  1;
%e A276997      6,  1,  1;
%e A276997      1,  2,  2,  1;
%e A276997     60,  1,  1,  1, 1;
%e A276997      1,  6,  2,  3, 1, 1;
%e A276997    504,  4,  4,  1, 1, 1, 1;
%e A276997      1, 24,  8, 12, 2, 2, 2, 1;
%e A276997   2160, 18,  9,  3, 2, 1, 3, 1, 1;
%p A276997 A276997_row := proc(n) local p;
%p A276997 p := (n,x) -> CompleteBellB(n,0,seq((k-2)!*bernoulli(k,x),k=2..n)):
%p A276997 seq(denom(coeff(p(n,x),x,k)), k=0..n) end:
%p A276997 seq(A276997_row(n), n=0..11);
%t A276997 CompleteBellB[n_, zz_] := Sum[BellY[n, k, zz[[1 ;; n-k+1]]], {k, 1, n}];
%t A276997 p[n_, x_] := CompleteBellB[n, Join[{0}, Table[(k-2)! BernoulliB[k, x], {k, 2, n}]]];
%t A276997 row[0] = {1}; row[1] = {1, 1}; row[n_] := CoefficientList[p[n, x], x] // Denominator;
%t A276997 Table[row[n], {n, 0, 11}] // Flatten (* _Jean-François Alcover_, Sep 09 2018 *)
%Y A276997 Cf. A276996 (numerators), A220411.
%K A276997 nonn,frac,tabl
%O A276997 0,4
%A A276997 _Peter Luschny_, Oct 01 2016