|
|
A100517
|
|
Denominator of Sum_{k=0..n} 1/binomial(n,k)^2.
|
|
5
|
|
|
1, 1, 4, 9, 72, 10, 3600, 1575, 2800, 1764, 14112, 13475, 34927200, 2316600, 192192, 4459455, 4994589600, 262061800, 735869534400, 17476901442, 422721728, 353723760, 31127690880, 10150725585, 59637542956992, 2205530434800, 155748568976000, 50956005028500
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
REFERENCES
|
H. W. Gould, Combinatorial Identities, Morgantown, 1972, p. 50, formula (5.2).
|
|
LINKS
|
|
|
FORMULA
|
a(n) = denominator( 3*(n+1)^2/((n+2)*(2*n+3)*Catalan(n+1)) * Sum_{k=1..n+1} binomial(2*k, k)/k ). - G. C. Greubel, Jun 24 2022
|
|
EXAMPLE
|
1, 2, 9/4, 20/9, 155/72, 21/10, 7441/3600, 3224/1575, 5697/2800, 3575/1764, 28523/14112, 27183/13475, 70357417/34927200, 4661447/2316600, ... = A100516/A100517
|
|
MATHEMATICA
|
Table[Sum[1/Binomial[n, k]^2, {k, 0, n}], {n, 0, 30}]//Denominator (* Harvey P. Dale, Apr 01 2019 *)
|
|
PROG
|
(Magma) [Denominator( (&+[1/Binomial[n, k]^2: k in [0..n]]]) ): n in [0..40]]; // G. C. Greubel, Jun 24 2022
(SageMath) [denominator(sum(1/binomial(n, k)^2 for k in (0..n))) for n in (0..40)] # G. C. Greubel, Jun 24 2022
(PARI) a(n) = denominator(sum(k=0, n, 1/binomial(n, k)^2)); \\ Michel Marcus, Jun 24 2022
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,frac
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|