A219563 Sum(binomial(n+k,k)^5, k=0..n).
1, 33, 8020, 3301025, 1733984376, 1048567813062, 694995078406056, 491336887915201185, 364377975224032162000, 280380150421755638519408, 222165159124597435189467696, 180288439972217748901049985158, 149230751849318301857448761484400, 125602423480863080624602495191566250
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,k]^5, {k,0,n}], {n,0,20}]
Formula
a(n) ~ 2^(10*n+5)/(31*(Pi*n)^(5/2)).