|
|
A184890
|
|
a(n) = C(2n,n) * (5^n/n!^2) * Product_{k=0..n-1} (5k+2)*(5k+3).
|
|
2
|
|
|
1, 60, 12600, 3640000, 1218262500, 443837394000, 170877396690000, 68390813462400000, 28171137810976875000, 11864338450927462500000, 5085530033605547526000000, 2211345876971860770960000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
A184889(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+2)*(10k+3).
a(n) ~ sqrt(5 + sqrt(5)) * 2^(2*n - 3/2) * 5^(3*n) / (Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Oct 07 2020
|
|
EXAMPLE
|
G.f.: A(x) = 1 + 60*x + 12600*x^2 + 3640000*x^3 +...
A(x)^(1/2) = 1 + 30*x + 5850*x^2 + 1644500*x^3 +...+ A184889(n)*x^n +...
|
|
MATHEMATICA
|
Table[Binomial[2*n, n] * 5^n / n!^2 * Product[(5*k + 2)*(5*k + 3), {k, 0, n - 1}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 07 2020 *)
|
|
PROG
|
(PARI) {a(n)=(2*n)!/n!^2*(5^n/n!^2)*prod(k=0, n-1, (5*k+2)*(5*k+3))}
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|