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) ~ 2^(12*n+6)/(63*Pi^3*n^3)
Generally (for q > 0), Sum_{k=0..n} C(n + k,k)^q is asymptotic to 2^((2*n+1)*q)/((2^q-1)*(Pi*n)^(q/2)) * (1 - q/(2*n)*(1/4+1/(2^q-1)^2) + O(1/n^2))
MATHEMATICA
Table[Sum[Binomial[n+k, k]^6, {k, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 23 2012
STATUS
approved