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

0,2

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^(10*n+5)/(31*(Pi*n)^(5/2)).

Mathematica

Table[Sum[Binomial[n+k, k]^5, {k, 0, n}], {n, 0, 20}]

Crossrefs

Cf. A001700, A112029, A112028, A219562, A219564.

Sequence in context: A210069 A316777 A057981 * A183237 A099828 A099827

Adjacent sequences: A219560 A219561 A219562 * A219564 A219565 A219566

Keyword

nonn

Author

Vaclav Kotesovec, Nov 23 2012

Status

approved