|
|
A004316
|
|
a(n) = binomial coefficient C(2n, n-10).
|
|
2
|
|
|
1, 22, 276, 2600, 20475, 142506, 906192, 5379616, 30260340, 163011640, 847660528, 4280561376, 21090682613, 101766230790, 482320623240, 2250829575120, 10363194502115, 47153358767970, 212327989773900, 947309492837400, 4191844505805495, 18412956934908690, 80347448443237920
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
10,2
|
|
REFERENCES
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 828.
|
|
LINKS
|
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
|
|
FORMULA
|
Sum_{n>=10} 1/a(n) = 59*Pi/(9*sqrt(3)) - 26565167/2450448.
Sum_{n>=10} (-1)^n/a(n) = 1322746*log(phi)/(5*sqrt(5)) - 697534881193/12252240, where phi is the golden ratio (A001622). (End)
|
|
MATHEMATICA
|
Table[Binomial[2*n, n-10], {n, 10, 30}] (* Amiram Eldar, Aug 27 2022 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|