A358496 a(n) = Sum_{k=0..n} binomial(binomial(n, k), k).

1, 2, 3, 7, 24, 176, 2623, 79479, 5141566, 669156932, 178757299486, 104033138190939, 125893536876304530, 320091464865316176891, 1828276720220263211454403, 22393381352339181425954204921, 582288411818399885839904060337943, 34678571156322738984042119670750665153

Offset: 0

Author

Vaclav Kotesovec, Nov 19 2022

Keywords

• nonn

Crossrefs

Cf. A167008, A220359, A357871, A358495.

Programs

Mathematica

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

PARI

a(n) = sum(k=0, n, binomial(binomial(n, k), k)); \\ Michel Marcus, Nov 19 2022

Formula

Limit_{n->infinity} a(n)^(1/n^2) = r^(r^2/(1-2*r)) = 1.533628065110458582..., where r = A220359 = 0.70350607643066243096929661621777... is the real root of the equation (1-r)^(2*r-1) = r^(2*r).