login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A075351 a(n) = floor(2*binomial(n+1,2)!/(binomial(n,2)!*n*(n^2+1))). 2
1, 1, 8, 148, 5544, 351982, 34100352, 4692680418, 871465795200, 210173265448681, 63895600819814400, 23912071579876921820, 10804489706894562201600, 5800208625625936700452385, 3649548011303182127557017600, 2660422068287264314770502524513 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Consider the harmonic progression 1, 1/2, 1/3, 1/4, 1/5, ...; then a(n) = floor(reciprocal of the sum of next n terms of this harmonic progression).

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..225

EXAMPLE

a(4) = floor(7*8*9*10/(7+8+9+10)) = floor(5040/34) = 148.

MAPLE

a:=n->floor((n*(n+1)/2)!/(n*(n-1)/2)!/(n*(n^2+1)/2)): seq(a(n), n=1..16); # Emeric Deutsch, Aug 04 2005

MATHEMATICA

Table[Floor[2*Binomial[n+1, 2]!/(Binomial[n, 2]!*n*(n^2+1))], {n, 1, 25}] (* G. C. Greubel, Mar 07 2019 *)

PROG

(PARI) k=1; for(n=0, 20, p=1; s=0; for(i=k, k+n, s=s+i; p=p*i); k=k+n+1; print1(floor(p/s)", "))

(MAGMA) [Floor(2*Gamma((n^2+n+2)/2)/(Gamma((n^2-n+2)/2)*n*(n^2+1))): n in [1..25]]; // G. C. Greubel, Mar 07 2019

(Sage) [floor(2*factorial((n+1)*n/2)/(factorial(n*(n-1)/2)*n*(n^2+1))) for n in (1..25)] # G. C. Greubel, Mar 07 2019

CROSSREFS

Cf. A075350.

Sequence in context: A116876 A218305 A244028 * A302063 A220559 A264642

Adjacent sequences:  A075348 A075349 A075350 * A075352 A075353 A075354

KEYWORD

nonn

AUTHOR

Amarnath Murthy, Sep 19 2002

EXTENSIONS

More terms from Ralf Stephan, Mar 31 2003

Name edited by Jon E. Schoenfield, Mar 07 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 1 12:40 EST 2021. Contains 349429 sequences. (Running on oeis4.)