login
A184896
a(n) = C(2n,n) * (7^n/n!^2) * Product_{k=0..n-1} (7k+1)*(7k+6).
6
1, 84, 45864, 35672000, 32445913500, 32247604076688, 33935228690034672, 37165308416775931392, 41919854708375196052500, 48365506771435816732770000, 56812832722107710740048677120, 67715433011522917282547695380480
OFFSET
0,2
FORMULA
Self-convolution of A184895, where A184895(n) = (7^n/n!^2) * Product_{k=0..n-1} (14k+1)*(14k+6).
a(n) ~ sin(Pi/7) * 2^(2*n) * 7^(3*n) / (Pi*n)^(3/2). - Vaclav Kotesovec, Oct 23 2020
EXAMPLE
G.f.: A(x) = 1 + 84*x + 45864*x^2 + 35672000*x^3 +...
A(x)^(1/2) = 1 + 42*x + 22050*x^2 + 16909900*x^3 +...+ A184895(n)*x^n +...
PROG
(PARI) {a(n)=(2*n)!/n!^2*(7^n/n!^2)*prod(k=0, n-1, (7*k+1)*(7*k+6))}
CROSSREFS
Sequence in context: A184126 A185403 A269897 * A203093 A290274 A289557
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jan 25 2011
STATUS
approved