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

0,4

Comments

For formulas and references see A276996.

Compare T(n,0) with A220411.

Links

Table of n, a(n) for n=0..77.

Example

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;

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 *)

Crossrefs

Cf. A276996 (numerators), A220411.

Sequence in context: A126795 A348929 A334491 * A324394 A064793 A355925

Adjacent sequences: A276994 A276995 A276996 * A276998 A276999 A277000

Keyword

nonn,frac,tabl

Author

Peter Luschny, Oct 01 2016

Status

approved