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

0,2

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).

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)

Maple

seq(6*bernoulli(2, 2^i), i=0..24);

Mathematica

6*BernoulliB[2, 2^Range[0, 30]] (* Paolo Xausa, Sep 16 2024 *)

Prog

(Magma) [6 * (4^n - 2^n) + 1: n in [0..40]]; // Vincenzo Librandi, Apr 25 2011

Crossrefs

Cf. A020528.

Sequence in context: A107963 A006230 A066110 * A146618 A220414 A139157

Adjacent sequences: A020524 A020525 A020526 * A020528 A020529 A020530

Keyword

nonn,easy

Author

Simon Plouffe

Status

approved