A319105 Expansion of e.g.f. Product_{k>=0} 1/(1 - x^(2^k))^(1/2^k).

1, 1, 3, 9, 51, 255, 1845, 12915, 129465, 1165185, 13338675, 146725425, 2023126875, 26300649375, 405966485925, 6089497288875, 110674075136625, 1881459277322625, 36921598987147875, 701510380755809625, 15370603498046671875, 322782673458980109375, 7608990209632029343125, 175006774821536674891875

Offset: 0

Author

Ilya Gutkovskiy, Sep 10 2018

Keywords

• nonn

Crossrefs

Cf. A001511, A018819, A028342.

Programs

Mathematica

nmax = 23; CoefficientList[Series[Product[1/(1 - x^2^k)^(1/2^k), {k, 0, Ceiling[Log[2, nmax]]}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 23; CoefficientList[Series[Exp[Sum[(IntegerExponent[k, 2] + 1) x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = (n - 1)! Sum[(IntegerExponent[k, 2] + 1) a[n - k]/(n - k)!, {k, 1, n}]; a[0] = 1; Table[a[n], {n, 0, 23}]

Formula

E.g.f.: exp(Sum_{k>=1} A001511(k)*x^k/k).