A020527 2nd Bernoulli polynomial evaluated at powers of 2 (multiplied by 6).
1, 13, 73, 337, 1441, 5953, 24193, 97537, 391681, 1569793, 6285313, 25153537, 100638721, 402604033, 1610514433, 6442254337, 25769410561, 103078428673, 412315287553, 1649264295937, 6597063475201, 26388266483713, 105553091100673, 422212414734337, 1688849759600641, 6755399239729153
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..170
- Index entries for sequences related to Bernoulli numbers.
- Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
Crossrefs
Cf. A020528.
Programs
-
Magma
[6 * (4^n - 2^n) + 1: n in [0..40]]; // Vincenzo Librandi, Apr 25 2011
-
Maple
seq(6*bernoulli(2,2^i),i=0..24);
-
Mathematica
6*BernoulliB[2, 2^Range[0, 30]] (* Paolo Xausa, Sep 16 2024 *)
Formula
a(n) = 6*(4^n - 2^n) + 1. - Ralf Stephan, Apr 06 2004
G.f.: (-1 - 6*x + 4*x^2)/((x-1)*(2*x-1)*(4*x-1)). - R. J. Mathar, Jun 11 2013
From Elmo R. Oliveira, Sep 12 2024: (Start)
E.g.f.: exp(x)*(6*exp(x)*(exp(2*x) - 1) + 1).
a(n) = 7*a(n-1) - 14*a(n-2) + 8*a(n-3) for n > 2. (End)