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A189998 Numerator of h(n+5) - h(n) where h(n) = Sum_{k=1..n} (1/k) are the Harmonic numbers. 3
137, 29, 153, 743, 1879, 1627, 15797, 2021, 11899, 25381, 7793, 2627, 124877, 26987, 68879, 65003, 107699, 66167, 482897, 16167, 77293, 412561, 323959, 94781, 1323137, 255127, 587299, 504563, 255733 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

a(n) = Numerator of (5*n^4 + 60*n^3 + 255*n^2 + 450*n + 274)/((n+1)*(n+2)*(n+3)*(n+4)*(n+5)).

(5*n^4 + 60*n^3 + 255*n^2 + 450*n + 274)/a(n) can be factored into 2^p(n)* 3^q(n) where p(n) is a sequence of period 4 repeating [1,2,1,3] and q(n) is of period 9,repeating [0,2,2,0,1,1,0,1,1].

p(n)= A131743(n) + 1.

q(n)= A011655(n) + [0,2,2,0,0,0,0,0,0]

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = (5*n^4 + 60*n^3 + 255*n^2 + 450*n + 274)/(2^q(n)*3^(P(9,n-1) +P(9,n-2) +(1-P(3,n))), where q(n) = (1-(-1)^n)*(3+i^(n+1))/4 + 1 and P(k,n) = floor(1/2*cos(2*n*Pi/k)+1/2).

MAPLE

h:= n->sum(1/k, k=1..n):seq(numer(h(n+5)-h(n)), n=0..28);

q:=n-> (1-(-1)^n)*(3+I^(n+1))/4+1:

P:=(k, n)-> floor(1/2*cos(2*n*Pi/k)+1/2):

seq( (5*n^4+60*n^3+255*n^2+450*n+274)/(2^q(n)*3^(P(9, n-1)+P(9, n-2)+(1-P(3, n))), n=0..28)

MATHEMATICA

Numerator[Table[HarmonicNumber[n+5]-HarmonicNumber[n], {n, 0, 30}]] (* Harvey P. Dale, Sep 15 2016 *)

PROG

(MAGMA) [137] cat [Numerator(HarmonicNumber(n+5)-HarmonicNumber(n)): n in [0..30]]; // G. C. Greubel, Jan 11 2018

CROSSREFS

Sequence in context: A134885 A259680 A082726 * A138358 A138329 A066477

Adjacent sequences:  A189995 A189996 A189997 * A189999 A190000 A190001

KEYWORD

nonn

AUTHOR

Gary Detlefs, May 03 2011

STATUS

approved

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Last modified January 26 13:09 EST 2022. Contains 350598 sequences. (Running on oeis4.)