A069993 a(n) = 2^(2n+1)*Sum_{k=1..2*n} binomial(2n+1,k)*Bernoulli(k)/2^k.

5, 27, 121, 503, 2037, 8179, 32753, 131055, 524269, 2097131, 8388585, 33554407, 134217701, 536870883, 2147483617, 8589934559, 34359738333, 137438953435, 549755813849, 2199023255511, 8796093022165, 35184372088787

Offset: 1

Author

Benoit Cloitre, May 01 2002

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Crossrefs

Cf. A024037. - Rolf Pleisch, Aug 09 2009

Programs

Magma

[2*(4^n-n)-1: n in [1..30]]; // Vincenzo Librandi, Jul 02 2011

Mathematica

LinearRecurrence[{6,-9,4},{5,27,121},30] (* Harvey P. Dale, Jul 03 2021 *)

PARI

for(n=1,30,print1(-2*4^n*sum(i=1,2*n+1,binomial(2*n+1,i)*bernfrac(i)/2^i),","))

PARI

Vec(x*(5 - 3*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)) + O(x^25)) \\ Colin Barker, May 30 2020

Formula

From Rolf Pleisch, Aug 09 2009: (Start)

a(n) = 2(4^n-n) - 1;

a(n) = 2*A024037(n) - 1.

(End)

From Colin Barker, May 30 2020: (Start)

G.f.: x*(5 - 3*x + 4*x^2) / ((1 - x)^2*(1 - 4*x)).

a(n) = 6*a(n-1) - 9*a(n-2) + 4*a(n-3) for n>3.

(End)