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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) 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 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 February 1 18:07 EST 2023. Contains 359995 sequences. (Running on oeis4.)