|
|
A060541
|
|
a(n) = binomial(4*n, 4).
|
|
3
|
|
|
1, 70, 495, 1820, 4845, 10626, 20475, 35960, 58905, 91390, 135751, 194580, 270725, 367290, 487635, 635376, 814385, 1028790, 1282975, 1581580, 1929501, 2331890, 2794155, 3321960, 3921225, 4598126, 5359095, 6210820, 7160245, 8214570, 9381251, 10668000, 12082785
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) = n*(2n-1)*(4n-1)*(4n-3)/3.
G.f.: x*(1+65*x+155*x^2+35*x^3) / (1-x)^5. - R. J. Mathar, Oct 03 2011
Sum_{n>=1} 1/a(n) = 6*log(2) - Pi.
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*sqrt(2)*log(sqrt(2)-1) - log(2) + (2*sqrt(2) - 3/2)*Pi. (End)
|
|
MATHEMATICA
|
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 70, 495, 1820, 4845}, 40] (* Harvey P. Dale, Jan 13 2015 *)
|
|
PROG
|
(PARI) a(n) = n*(2*n - 1)*(4*n - 1)*(4*n - 3)/3; \\ Harry J. Smith, Jul 06 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|