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A188386 Numerator(h(n+2)-h(n-1)), where h(n) is the n-th harmonic number sum(1/k, k=1..n). 7
11, 13, 47, 37, 107, 73, 191, 121, 299, 181, 431, 253, 587, 337, 767, 433, 971, 541, 1199, 661, 1451, 793, 1727, 937, 2027, 1093, 2351, 1261, 2699, 1441, 3071, 1633, 3467, 1837, 3887, 2053, 4331, 2281, 4799, 2521 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Denominator is listed in A033931. A027446 appears to be divisible by a(n).

The sequence lists also the largest odd divisors of 3*m^2-1 (A080663) for m>1. In fact, for m even, the largest odd divisor is 3*m^2-1 itself; for m odd, the largest odd divisor is (3*m^2-1)/2. From this follows the second formula given in Formula field. [Bruno Berselli, Aug 27 2013]

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1)

FORMULA

a(n) = numerator ((3*n^2+6*n+2)/(n*(n+1)*(n+2))).

a(n) = (3-(-1)^n)*(3*n^2+6*n+2)/4.

a(2n+1) = A158463(n+1), a(2n) = A003154(n+1).

G.f.: -x*(11+13*x+14*x^2-2*x^3-x^4+x^5) / ( (x-1)^3*(1+x)^3 ). - R. J. Mathar, Apr 09 2011

a(n) = numerator of coefficient of x^3 in the Maclaurin expansion of sin(x)*exp((n+1)*x). [Francesco Daddi, Aug 04 2011]

h(n+3) = 3/2+2*f(n)/((n+2)*(n+3)), where f(n)= sum((-1)^k*binomial(-3,k)/(n+1-k),k=0..n). [Gary Detlefs, Jul 17 2011]

a(n) = A213998(n+2,2). - Reinhard Zumkeller, Jul 03 2012

MAPLE

seq((3-(-1)^n)*(3*n^2+6*n+2)/4, n=1..100);

MATHEMATICA

Table[(3 - (-1)^n)*(3*n^2 + 6*n + 2)/4, {n, 40}] (* Wesley Ivan Hurt, Jan 29 2017 *)

Numerator[#[[4]]-#[[1]]]&/@Partition[HarmonicNumber[Range[0, 50]], 4, 1] (* or *) LinearRecurrence[{0, 3, 0, -3, 0, 1}, {11, 13, 47, 37, 107, 73}, 50] (* Harvey P. Dale, Dec 31 2017 *)

PROG

(MAGMA) [Numerator((3*n^2+6*n+2)/((n*(n+1)*(n+2)))): n in [1..50]]; // Vincenzo Librandi, Mar 30 2011

(Haskell)

import Data.Ratio ((%), numerator)

a188386 n = a188386_list !! (n-1)

a188386_list = map numerator $ zipWith (-) (drop 3 hs) hs

   where hs = 0 : scanl1 (+) (map (1 %) [1..])

-- Reinhard Zumkeller, Jul 03 2012

CROSSREFS

Cf. A033931, A027446, A003154, A158436, A001711.

Sequence in context: A108264 A023268 A154292 * A027450 A234799 A036295

Adjacent sequences:  A188383 A188384 A188385 * A188387 A188388 A188389

KEYWORD

nonn,easy,look

AUTHOR

Gary Detlefs, Mar 29 2011

STATUS

approved

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Last modified July 27 11:29 EDT 2021. Contains 346304 sequences. (Running on oeis4.)