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!)
A351280 a(n) = Sum_{k=0..n} k! * k^k * Stirling1(n,k). 4
1, 1, 7, 140, 5254, 318854, 28455182, 3506576856, 570360248856, 118356589567440, 30512901324706608, 9566812017770347152, 3584662956711860108352, 1581905384865801328253712, 812047187127758913474118032, 479763784808095613489811245568 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
E.g.f.: Sum_{k>=0} (k * log(1+x))^k.
a(n) ~ exp(-exp(-1)/2) * n! * n^n. - Vaclav Kotesovec, Feb 06 2022
MATHEMATICA
a[0] = 1; a[n_] := Sum[k! * k^k * StirlingS1[n, k], {k, 1, n}]; Array[a, 16, 0] (* Amiram Eldar, Feb 06 2022 *)
PROG
(PARI) a(n) = sum(k=0, n, k!*k^k*stirling(n, k, 1));
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*log(1+x))^k)))
CROSSREFS
Sequence in context: A297650 A085708 A054606 * A306628 A302912 A191956
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Feb 06 2022
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 July 14 19:43 EDT 2024. Contains 374323 sequences. (Running on oeis4.)