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A346200
a(n) = Sum_{k=0..n} (binomial(n+k,k) * binomial(n,k))^k.
1
1, 3, 43, 8913, 26762121, 1173960290163, 786113240166904651, 8613513810086378347343577, 1711294617015624229036545787666921, 6770959866814792643630677926543098580902523, 536479956775359246458147222888630941089874512707772963
OFFSET
0,2
FORMULA
a(n)^(1/n) ~ (1+r)^(r*n/2 - 1/4) / ((2*Pi*n)^r * (1-r)^(r*n/2 + r - 1/4)), where r = 0.9222727963503830123185148157257918806196371551687495361664171679710425... is the root of the equation (1-r)^(2*r-1) * (1+r)^(2*r+1) = r^(4*r).
MATHEMATICA
Table[Sum[(Binomial[n+k, k]*Binomial[n, k])^k, {k, 0, n}], {n, 0, 12}]
CROSSREFS
Cf. A336873.
Sequence in context: A309401 A190637 A287959 * A326970 A076361 A130408
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 10 2021
STATUS
approved