7,2

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=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.

(End)

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.

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 226.

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

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

T. D. Noe, Table of n, a(n) for n=7..100

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

Let P(n+5,X)=(X+1)(X+2)(X+3)...(X+n+5); then a(n) is the coefficient of X^6; or a(n)=P^(vi)(n+5,0)/6! - Benoit Cloitre (benoit7848c(AT)orange.fr), May 09 2002

A001234 := proc(n) abs(combinat[stirling1](n, 7)) ; end: seq(A001234(n), n=7..30) ; [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 06 2009]

(PARI) for(n=6, 50, print1(polcoeff(prod(i=1, n, x+i), 6, x), ", "))

sage: [stirling_number1(i, 7) for i in xrange(7, 22)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 27 2008

Cf. A008275 (Stirling1 triangle).

Sequence in context: A163195 A092708 A163198 this_sequence A145149 A062142 A107397

Adjacent sequences: A001231 A001232 A001233 this_sequence A001235 A001236 A001237

nonn,easy,new

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

More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 06 2009