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=1,n=9) ~ exp(-x)/x*(1 - 9/x + 90/x^2 - 990/x^3 + 11880/x^4 - 154440/x^5 + ...) leads to the sequence given above. See A163931 and A130534 for more information.

(End)

a(n) = (n+8)!/8!; e.g.f.: 1/(1-x)^9.

a:=n->mul(denom( (k+1)/(k+2) ), k=7..n): seq(a(n), n=6..22); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2008

a:=n->mul(numer( (k+1)/(k+2) ), k=8..n): seq(a(n), n=7..23); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 27 2008

restart: G(x):=1/(1-x)^9: f[0]:=G(x): for n from 1 to 16 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..16); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 01 2009]

Cf. A000142, A001710, A001715, A001720, A001725, A001730, A049388, A051379. a(n)= A051380(n, 0)*(-1)^n (first unsigned column of triangle).

Sequence in context: A143079 A165324 A082367 this_sequence A127769 A062815 A160569

Adjacent sequences: A049386 A049387 A049388 this_sequence A049390 A049391 A049392

easy,nonn

Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)