A218690 Sum_{k=0..n} C(n,k)^4*C(n+k,k)^2.
1, 5, 181, 9797, 616501, 45778505, 3678753205, 314352091205, 28154344881205, 2612340741982505, 249415797821914681, 24374175871569953225, 2428502737999745059381, 245952659136011117909897, 25260608441078125508484181, 2626023605592369669830217797
Offset: 0
Keywords
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
Programs
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Mathematica
Table[Sum[Binomial[n,k]^4*Binomial[n+k,k]^2,{k,0,n}],{n,0,20}]
Formula
a(n) ~ ((1+sqrt(5))/2)^(2*(5*n+4)-3/2)/(5^(1/4)*(2*Pi*n)^(5/2)*sqrt(2)).