OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
V. Kotesovec, Asymptotic of generalized Apery sequences with powers of binomial coefficients, Nov 04 2012
FORMULA
a(n) ~ (1+sqrt(2))^(6*(2n+1))/(2^(17/4)*(Pi*n)^(11/2)*sqrt(3))
Generally, Sum_{k=0..n} C(n,k)^p*C(n+k,k)^p is asymptotic to (1+sqrt(2))^(p*(2*n+1))/(2^(p/2+3/4)*(Pi*n)^(p-1/2)*sqrt(p)) * (1-(2*p-1)/(4*n)+(4*p^2+24*p-19)*sqrt(2)/(96*p*n))
MATHEMATICA
Table[Sum[Binomial[n, k]^6*Binomial[n+k, k]^6, {k, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 04 2012
STATUS
approved