A094950 Number of integer coefficients in n-th Bernoulli polynomial (including zeros).

1, 1, 2, 2, 4, 3, 4, 4, 5, 7, 8, 8, 10, 8, 8, 8, 12, 9, 14, 12, 13, 15, 14, 12, 17, 16, 14, 18, 22, 21, 16, 16, 24, 24, 24, 27, 34, 28, 26, 26, 30, 25, 30, 28, 28, 32, 26, 26, 35, 32, 31, 37, 33, 27, 36, 39, 45, 46, 39, 39, 43, 40, 32, 32, 47, 51, 54, 47, 45, 49, 51

Offset

0,3

Links

Robert Israel, Table of n, a(n) for n = 0..5160

Example

B(5,x) = x^5 - 5/2*x^4 + 5/3*x^3 + 0*x^2 - 1/6*x + 0 hence a(5) = 3

Maple

f:= proc(n) local B;
  B:= bernoulli(n, x);
  nops(select(t -> coeff(B, x, t)::integer, [$0..degree(B)]))
end proc:
map(f, [$0..100]); # Robert Israel, Aug 28 2018

Mathematica

a[n_] := Select[CoefficientList[BernoulliB[n, x], x], IntegerQ] // Length;
a /@ Range[0, 100] (* Jean-François Alcover, Aug 26 2020 *)

Prog

(PARI) B(n, x)=sum(i=0, n, binomial(n, i)*bernfrac(i)*x^(n-i)); a(n)=sum(i=0, n, if(frac(polcoeff(B(n, x), i)), 0, 1))

Crossrefs

Sequence in context: A087808 A217754 A319397 * A087874 A363341 A166267

Adjacent sequences: A094947 A094948 A094949 * A094951 A094952 A094953

Keyword

nonn

Author

Benoit Cloitre, Jun 19 2004

Status

approved