6,2

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=1,n=7) ~ exp(-x)/x*(1 - 7/x + 56/x^2 - 504/x^3 + 5040/x^4 - 55440/x^5 + 665280/x^6 - 8648640/x^7 + ...) leads to the sequence given above. See A163931 and A130534 for more information.

(End)

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

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

Mitrinovic, D. S.; Mitrinovic, R. S.; Tableaux d'une classe de nombres relies aux nombres de Stirling. II. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. Fiz. No. 107-108 1963 1-77.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 266

Index entries for sequences related to factorial numbers

E.g.f. if offset 0: 1/(1-x)^7.

a:=n->mul(denom( (k+1)/(k+2) ), k=5..n): seq(a(n), n=4..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2008

a:=n->mul(numer( (k+1)/(k+2) ), k=6..n): seq(a(n), n=5..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2008

restart: G(x):=1/(1-x)^7: f[0]:=G(x): for n from 1 to 14 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..14); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 01 2009]

f[n_]:=n!/6!; Array[f, 4!, 6] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2009]

Cf. A051338, A051379. a(n)= A051339(n-6, 0)*(-1)^n (first unsigned column of triangle).

Sequence in context: A165322 A082305 A144263 this_sequence A087751 A099345 A110830

Adjacent sequences: A001727 A001728 A001729 this_sequence A001731 A001732 A001733

nonn

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