A306947 Expansion of e.g.f. Product_{k>=0} 1/(1 - x^(2^k)/2^k).

1, 1, 3, 9, 48, 240, 1620, 11340, 103320, 929880, 9865800, 108523800, 1362160800, 17708090400, 253361908800, 3800428632000, 63340477200000, 1076788112400000, 19769829743664000, 375626765129616000, 7640832869429760000, 160457490258024960000, 3559701523615997760000

Offset

0,3

Links

Table of n, a(n) for n=0..22.

Formula

a(n) ~ c * n!, where c = A065446 = 1/A048651 = 1/QPochhammer[1/2] = 3.4627466194550636115379573429244311645407579... - Vaclav Kotesovec, Mar 18 2019

Mathematica

nmax = 22; CoefficientList[Series[Product[1/(1 - x^2^k/2^k), {k, 0, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 22; CoefficientList[Series[Exp[Sum[Sum[Boole[IntegerQ[Log[2, d]]] d^(1 - k/d), {d, Divisors[k]}] x^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, (n - 1)! Sum[Sum[Boole[IntegerQ[Log[2, d]]] d^(1 - k/d), {d, Divisors[k]}] a[n - k]/(n - k)!, {k, 1, n}]]; Table[a[n], {n, 0, 22}]

Crossrefs

Cf. A007841, A319105.

Sequence in context: A102929 A105458 A366485 * A183952 A298308 A370426

Adjacent sequences: A306944 A306945 A306946 * A306948 A306949 A306950

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 17 2019

Status

approved