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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
OFFSET
1,1
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)
MATHEMATICA
LinearRecurrence[{6, -9, 4}, {5, 27, 121}, 30] (* Harvey P. Dale, Jul 03 2021 *)
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
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, May 01 2002
STATUS
approved