login
This site is supported by donations to The OEIS Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A001723 Generalized Stirling numbers.
(Formerly M5189 N2256)
2
1, 26, 485, 8175, 134449, 2231012, 37972304, 668566300, 12230426076, 232959299496, 4623952866312, 95644160132976, 2060772784375824, 46219209678691200, 1078100893671811200, 26129183717351462400, 657337657573760947200, 17147815411007234188800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The asymptotic expansion of the higher order exponential integral E(x,m=4,n=5) ~ exp(-x)/x^4*(1 - 26/x + 485/x^2 - 8175/x^3 + 134449/x^4 - 2231012/x^5 + ...) leads to the sequence given above. See A163931 and A163934 for more information. - Johannes W. Meijer, Oct 20 2009

REFERENCES

Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

T. D. Noe, Table of n, a(n) for n = 0..100

FORMULA

a(n)=sum((-1)^(n+k)*binomial(3+k, 3)*5^k*stirling1(n+3, k+3), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004

If we define f(n,i,a)=sum(binomial(n,k)*stirling1(n-k,i)*product(-a-j,j=0..k-1),k=0..n-i), then a(n-3) = |f(n,3,5)|, for n>=3. [From Milan Janjic, Dec 21 2008]

MATHEMATICA

Table[Sum[(-1)^(n + k)*Binomial[k + 3, 3]*5^k*StirlingS1[n + 3, k + 3], {k, 0, n}], {n, 0, 20}] (* T. D. Noe, Aug 10 2012 *)

CROSSREFS

Sequence in context: A021334 A018208 A240190 * A163201 A205990 A230247

Adjacent sequences:  A001720 A001721 A001722 * A001724 A001725 A001726

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004

STATUS

approved

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 January 16 03:14 EST 2019. Contains 319184 sequences. (Running on oeis4.)