The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A194004 E.g.f.: A(x) = -log(3-exp(x)-exp(x^2)). 0
0, 1, 4, 12, 86, 590, 6032, 66948, 913754, 13855542, 239928992, 4579666916, 96564964322, 2216227508118, 55168605200984, 1478010072581076, 42439794637684826, 1299629513716412246, 42289878531064635632, 1456983891928235324292, 52986585444052122288146 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
a(n) = n!*sum(k=1..n, (k-1)!*sum(j=0..k, sum(m=floor((k-j)/2)..(n-j)/2, (stirling2(n-2*m,j)*stirling2(m,k-j))/((n-2*m)!*(m!))))).
a(n) ~ (n-1)!/r^n, where r = 0.522452131474223... is the root of the equation exp(r)+exp(r^2) = 3. - Vaclav Kotesovec, Jun 27 2013
MATHEMATICA
CoefficientList[Series[-Log[3-E^x-E^(x^2)], {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)
PROG
(Maxima)
a(n):=n!*sum((k-1)!*sum(sum((stirling2(n-2*m, j)*stirling2(m, k-j))/((n-2*m)!*(m!)), m, floor((k-j)/2), (n-j)/2), j, 0, k), k, 1, n);
CROSSREFS
Sequence in context: A226960 A081214 A331087 * A064280 A203379 A209031
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Aug 10 2011
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 19 00:35 EDT 2024. Contains 372666 sequences. (Running on oeis4.)