OFFSET
0,2
FORMULA
Self-convolution of A184891, where
. A184891(n) = (5^n/n!^2) * Product_{k=0..n-1} (10k+1)*(10k+4).
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 + 40*x + 8100*x^2 + 2310000*x^3 +...
A(x)^(1/2) = 1 + 20*x + 3850*x^2 + 1078000*x^3 +...+ A184891(n)*x^n +...
MATHEMATICA
Table[Binomial[2*n, n] * 5^n / n!^2 * Product[(5*k + 1)*(5*k + 4), {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+1)*(5*k+4))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 25 2011
STATUS
approved