Search: id:A001233
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%I A001233 M5114 N2216
%S A001233 1,21,322,4536,63273,902055,13339535,206070150,3336118786,
%T A001233 56663366760,1009672107080,18861567058880,369012649234384,
%U A001233 7551527592063024
%N A001233 Un signed Stirling numbers of first kind s(n,6).
%C A001233 Contribution from Johannes W. Meijer (meijgia(AT)hotmail.com), Oct 20 
               2009: (Start)
%C A001233 The asymptotic expansion of the higher order exponential integral E(x,
               m=6,n=1) ~ exp(-x)/x^6*(1 - 21/x + 322/x^2 - 4536/x^3 + 63273/x^4 
               - ...) leads to the sequence given above. See See A163931 for E(x,
               m,n) information and A163932 for a Maple procedure for the asymptotic 
               expansion.
%C A001233 (End)
%D A001233 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 833.
%D A001233 F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied 
               Tables, Cambridge, 1966, p. 226.
%D A001233 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A001233 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A001233 T. D. Noe, <a href="b001233.txt">Table of n, a(n) for n=6..100</a>
%H A001233 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%F A001233 Let P(n+4,X)=(X+1)(X+2)(X+3)...(X+n+4); then a(n) is the coefficient 
               of X^5; or a(n)=P'''''(n+4,0)/5! - Benoit Cloitre (benoit7848c(AT)orange.fr), 
               May 09 2002
%F A001233 E.g.f.: (-log(1-x))^6/6! or (1-x)^-1 * (-log(1-x))^5.
%F A001233 a(n) is coefficient of x^(n+6) in (-log(1-x))^6, multiplied by (n+6)!/
               6!.
%e A001233 (-log(1-x))^6 = x^6 + 3*x^7 + 23/4*x^8 + 9*x^9 + ...
%o A001233 (PARI) for(n=5,50,print1(polcoeff(prod(i=1,n,x+i),5,x),","))
%o A001233 sage: [stirling_number1(i,6) for i in xrange(6,22)] - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 27 2008
%Y A001233 Cf. A000254, A000399, A000454, A000482, A008275 (Stirling1 triangle).
%Y A001233 Sequence in context: A036737 A141267 A016262 this_sequence A145148 A016260 
               A011810
%Y A001233 Adjacent sequences: A001230 A001231 A001232 this_sequence A001234 A001235 
               A001236
%K A001233 nonn,easy,more
%O A001233 6,2
%A A001233 N. J. A. Sloane (njas(AT)research.att.com).

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