A369406 a(n) = Sum_{k=0..n} binomial(n,k^3).

1, 2, 3, 4, 5, 6, 7, 8, 10, 19, 56, 177, 508, 1301, 3018, 6451, 12887, 24328, 43777, 75602, 125991, 203512, 319793, 490338, 735496, 1081601, 1562302, 2220104, 3108162, 4292581, 5857016, 7920222, 10719709, 14991758, 23535855, 47071676, 124403657, 386938194, 1252225819

Offset: 0

Author

Ilya Gutkovskiy, Jan 22 2024

Keywords

• nonn

Comments

a(n) equals the number of subsets of [n] whose cardinalities are cube.

Binomial transform of the characteristic function of cubes A010057.

Partial sums of A280351.

Crossrefs

Cf. A010057, A003099, A280351.

Programs

Mathematica

Table[Sum[Binomial[n, k^3], {k, 0, n^(1/3)}], {n, 0, 38}]
nmax = 38; CoefficientList[Series[(1/(1 - x)) Sum[(x/(1 - x))^k^3, {k, 0, nmax}], {x, 0, nmax}], x]

Formula

G.f.: (1/(1 - x)) * Sum_{k>=0} (x/(1 - x))^(k^3).