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.

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, 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, 2, 1, 2, 1, 1, 1, 288, 32, 144, 12, 12, 4, 2, 1, 6, 2, 1

Offset: 0

Author

Peter Luschny, Oct 01 2016

Keywords

• nonn
• frac
• tabl

Comments

For formulas and references see A276996.

Compare T(n,0) with A220411.

Examples

			Triangle starts:
     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, 2, 2, 2, 1;
  2160, 18,  9,  3, 2, 1, 3, 1, 1;
		

Crossrefs

Cf. A276996 (numerators), A220411.

Programs

Maple

A276997_row := proc(n) local p;
p := (n,x) -> CompleteBellB(n,0,seq((k-2)!*bernoulli(k,x),k=2..n)):
seq(denom(coeff(p(n,x),x,k)), k=0..n) end:
seq(A276997_row(n), n=0..11);

Mathematica

CompleteBellB[n_, zz_] := Sum[BellY[n, k, zz[[1 ;; n-k+1]]], {k, 1, n}];
p[n_, x_] := CompleteBellB[n, Join[{0}, Table[(k-2)! BernoulliB[k, x], {k, 2, n}]]];
row[0] = {1}; row[1] = {1, 1}; row[n_] := CoefficientList[p[n, x], x] // Denominator;
Table[row[n], {n, 0, 11}] // Flatten (* Jean-François Alcover, Sep 09 2018 *)