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A069993 a(n) = 2^(2n+1)*Sum_{k=1..2*n} binomial(2n+1,k)*Bernoulli(k)/2^k. 1
5, 27, 121, 503, 2037, 8179, 32753, 131055, 524269, 2097131, 8388585, 33554407, 134217701, 536870883, 2147483617, 8589934559, 34359738333, 137438953435, 549755813849, 2199023255511, 8796093022165, 35184372088787 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

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)

PROG

(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

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

CROSSREFS

Cf. A024037. - Rolf Pleisch, Aug 09 2009

Sequence in context: A201436 A202508 A129868 * A249995 A009027 A275540

Adjacent sequences:  A069990 A069991 A069992 * A069994 A069995 A069996

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, May 01 2002

STATUS

approved

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Last modified April 18 15:04 EDT 2021. Contains 343089 sequences. (Running on oeis4.)