A330198 Expansion of e.g.f. Product_{k>=1} 1 / (2 - exp(x^k)).

1, 1, 5, 25, 195, 1521, 16713, 179425, 2432139, 33902149, 546239793, 9158893173, 173742256251, 3402217292137, 73413011744985, 1653326843775193, 40118677865954475, 1014971456865241197, 27429061245764539521, 770776923753566642365, 22928146838491708702395

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

E.g.f.: A(x) = Product_{k>=1} B(x^k), where B(x) = e.g.f. of Fubini numbers (A000670).

E.g.f.: Product_{j>=1} 1 / (1 - Sum_{i>=1} x^(i*j) / i!).

E.g.f.: exp(Sum_{k>=1} Sum_{d|k} (exp(x^(k/d)) - 1)^d / d).

a(n) ~ n! * c / (2 * (log(2))^(n+1)), where c = Product_{k>=2} (1/(2 - exp(log(2)^k)) = 10.38787833857244631... - Vaclav Kotesovec, Dec 11 2019

Mathematica

nmax = 20; CoefficientList[Series[Product[1/(2 - Exp[x^k]), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Exp[Sum[Sum[(Exp[x^(k/d)] - 1)^d/d, {d, Divisors[k]}], {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!

Crossrefs

Cf. A000262, A000670, A209903.

Sequence in context: A096245 A294363 A294213 * A346269 A337041 A254335

Adjacent sequences: A330195 A330196 A330197 * A330199 A330200 A330201

Keyword

nonn

Author

Ilya Gutkovskiy, Dec 05 2019

Status

approved