OFFSET
0,3
FORMULA
a(n) = Sum_{k=0..A003056(n)} q(n,k) * 8^(n-k), where q(n,k) is the number of partitions of n into k distinct parts.
a(n) ~ (-polylog(2, -1/8))^(1/4) * 8^n * exp(2*sqrt(-polylog(2, -1/8)*n)) / (6*sqrt(Pi/8)*n^(3/4)). - Vaclav Kotesovec, May 09 2021
MATHEMATICA
nmax = 22; CoefficientList[Series[Product[(1 + 8^(k - 1) x^k), {k, 1, nmax}], {x, 0, nmax}], x]
Table[Sum[Length[Select[IntegerPartitions[n, {k}], UnsameQ @@ # &]] 8^(n - k), {k, 0, Floor[(Sqrt[8 n + 1] - 1)/2]}], {n, 0, 22}]
PROG
(PARI) seq(n)={Vec(prod(k=1, n, 1 + 8^(k-1)*x^k + O(x*x^n)))} \\ Andrew Howroyd, May 08 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 08 2021
STATUS
approved