login
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
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
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
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