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URL: https://oeis.org/A358496

⇱ A358496 - OEIS

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A358496
a(n) = Sum_{k=0..n} binomial(binomial(n, k), k).
1
1, 2, 3, 7, 24, 176, 2623, 79479, 5141566, 669156932, 178757299486, 104033138190939, 125893536876304530, 320091464865316176891, 1828276720220263211454403, 22393381352339181425954204921, 582288411818399885839904060337943, 34678571156322738984042119670750665153
OFFSET
0,2
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).
MATHEMATICA
Table[Sum[Binomial[Binomial[n, k], k], {k, 0, n}], {n, 0, 20}]
PROG
(PARI) a(n) = sum(k=0, n, binomial(binomial(n, k), k)); \\ Michel Marcus, Nov 19 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Nov 19 2022
STATUS
approved