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
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
D. S. Mitrinovic and R. S. Mitrinovic, Tableaux d'une classe de nombres reliés aux nombres de Stirling, Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 77 1962, 77 pp.
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n+k)*binomial(3+k, 3)*5^k*Stirling1(n+3, k+3). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*Stirling1(n-k,i)*Product_{j=0..k-1} (-a-j), then a(n-3) = |f(n,3,5)|, for n >= 3. - 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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004
Name clarified by Sean A. Irvine and Natalia L. Skirrow, Nov 10 2025
STATUS
approved
