5,2

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=6) ~ exp(-x)/x*(1 - 6/x + 42/x^2 - 336/x^3 + 3024/x^4 - 30240/x^5 + 332640/x^6 - 3991680/x^7 + ...) leads to the sequence given above. See A163931 and A130534 for more information.

(End)

a(n) = A173333(n,5). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 19 2010]

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 265

W. Lang, On generalizations of Stirling number triangles, J. Integer Seqs., Vol. 3 (2000), #00.2.4.

Alexsandar Petojevic, The Function vM_m(s; a; z) and Some Well-Known Sequences, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7

Index entries for sequences related to factorial numbers

E.g.f.: if offset 0: 1/(1-x)^6.

a:=n->mul(numer( (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(denom( (k+1)/(k+2) ), k=4..n): seq(a(n), n=3..17); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2008

restart: G(x):=1/(1-x)^6: f[0]:=G(x): for n from 1 to 18 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..17); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 01 2009]

lst={}; Do[AppendTo[lst, n!/5! ], {n, 5, 5!}]; lst ...and/or... s=1; lst={s}; Do[s+=n*s; AppendTo[lst, s], {n, 5, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 25 2008]

(Other) sage: [binomial(n, 5)*factorial (n-5) for n in xrange(5, 20)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 07 2009]

a(n)= A049374(n-4), n >= 1 (first column of triangle). Cf. A049460, A051339. a(n)= A051338(n-5, 0)*(-1)^(n-1) (first unsigned column of triangle).

Sequence in context: A082302 A144223 A029588 this_sequence A123510 A132804 A074017

Adjacent sequences: A001722 A001723 A001724 this_sequence A001726 A001727 A001728

nonn

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