login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A330020 Expansion of e.g.f. Sum_{k>=1} x^k / (k! * (1 - x^k)^k). 0

%I

%S 1,3,7,49,121,2161,5041,127681,725761,12852001,39916801,2917918081,

%T 6227020801,392423391361,4740319584001,122053759027201,

%U 355687428096001,57808258040332801,121645100408832001,18854997267794688001,289799177540640768001,7306005040298918553601

%N Expansion of e.g.f. Sum_{k>=1} x^k / (k! * (1 - x^k)^k).

%F a(n) = n! * Sum_{d|n} (d + n/d - 2)! / (d! * (d - 1)! * (n/d - 1)!).

%t nmax = 22; CoefficientList[Series[Sum[x^k/(k! (1 - x^k)^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]! // Rest

%t a[n_] := n! Sum[(d + n/d - 2)!/(d! (d - 1)! (n/d - 1)!), {d, Divisors[n]}]; Table[a[n], {n, 1, 22}]

%Y Cf. A057625, A157019, A327578, A327579.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Nov 27 2019

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified November 28 04:43 EST 2021. Contains 349400 sequences. (Running on oeis4.)