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%I M5202 N2264 #45 Feb 03 2022 00:28:08
%S 1,28,546,9450,157773,2637558,44990231,790943153,14409322928,
%T 272803210680,5374523477960,110228466184200,2353125040549984,
%U 52260903362512720,1206647803780373360,28939583397335447760
%N Unsigned Stirling numbers of the first kind s(n,7).
%C The asymptotic expansion of the higher order exponential integral E(x,m=7,n=1) ~ exp(-x)/x^7*(1 - 28/x + 546/x^2 - 9450/x^3 + 157773/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. - _Johannes W. Meijer_, Oct 20 2009
%D M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 834.
%D F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 226.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A001234/b001234.txt">Table of n, a(n) for n=7..100</a>
%H M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
%F Let P(n-1,X) = (X+1)(X+2)(X+3)...(X+n-1); then a(n) is the coefficient of X^6; or a(n) = P^(vi)(n-1,0)/6!. - _Benoit Cloitre_, May 09 2002 [Edited by _Petros Hadjicostas_, Jun 29 2020 to agree with the offset 7]
%F a(n) = det(|S(i+7,j+6)|, 1 <= i,j <= n-7), where S(n,k) are Stirling numbers of the second kind. - _Mircea Merca_, Apr 06 2013
%e G.f. = x^7 + 28*x^8 + 546*x^9 + 9450*x^10 + 157773*x^11 + 2637558*x^12 + ...
%p A001234 := proc(n) abs(combinat[stirling1](n,7)) ; end: seq(A001234(n),n=7..30) ; # _R. J. Mathar_, Nov 06 2009
%t Table[Abs[StirlingS1[n, 7]], {n, 7, 40}] (* _Jean-François Alcover_, Mar 24 2020 *)
%o (PARI) for(n=6,50,print1(polcoeff(prod(i=1,n,x+i),6,x),","))
%o (Sage) [stirling_number1(i,7) for i in range(7,22)] # _Zerinvary Lajos_, Jun 27 2008
%Y Cf. A008275 (Stirling1 triangle).
%Y Cf. A000254, A000399, A000454, A000482, A001233, A243569, A243570.
%K nonn,easy
%O 7,2
%A _N. J. A. Sloane_
%E More terms from _R. J. Mathar_, Nov 06 2009
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