0,2

Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 20 2009: (Start)

The asymptotic expansion of the higher order exponential integral E(x,m=6,n=2) ~ exp(-x)/x^6*(1 - 27/x + 511/x^2 - 8624/x^3 + 140889/x^4 - ...) leads to the sequence given above. See A163931 for E(x,m,n) information and A163932 for a Maple procedure for the asymptotic expansion.

(End)

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).

a(n)=sum((-1)^(n+k)*binomial(k+5, 5)*2^k*stirling1(n+5, k+5), k=0..n). - Borislav Crstici (bcrstici(AT)etv.utt.ro), Jan 26 2004

E.g.f.: (6-120*ln(1-x)+465*ln(1-x)^2-580*ln(1-x)^3+261*ln(1-x)^4-36*ln(1-x)^5)/(6*(1-x)^7). - Vladeta Jovovic (vladeta(AT)eunet.rs), Mar 01 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-5) = |f(n,5,2)|, for n>=5. [From Milan R. Janjic (agnus(AT)blic.net), Dec 21 2008]

Sequence in context: A020568 A021734 A019752 this_sequence A016887 A110896 A014928

Adjacent sequences: A001706 A001707 A001708 this_sequence A001710 A001711 A001712

nonn

N. J. A. Sloane (njas(AT)research.att.com).

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