A307680 Expansion of e.g.f. Product_{k>=1} (1 + x^k/(1 - x)^k)^(1/k).

1, 1, 3, 17, 131, 1239, 14029, 187627, 2906553, 50982929, 993806531, 21270277401, 496425262123, 12577053063847, 344382608381421, 10139294386051139, 319175215666010609, 10684742192933940897, 378662321114852778883, 14158327369578651838369, 557151639159864934384851

Offset

0,3

Links

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

Formula

E.g.f.: exp(Sum_{k>=1} A048272(k)*x^k/(k*(1 - x)^k)).

a(n) = Sum_{k=0..n} binomial(n-1,k-1)*A168243(k)*n!/k!.

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 17*x^3/3! + 131*x^4/4! + 1239*x^5/5! + 14029*x^6/6! + 187627*x^7/7! + 2906553*x^8/8! + ...

Mathematica

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

Crossrefs

Cf. A048272, A129519, A168243, A307679, A320564.

Sequence in context: A074524 A212280 A360581 * A305819 A163684 A363135

Adjacent sequences: A307677 A307678 A307679 * A307681 A307682 A307683

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 21 2019

Status

approved