A001234 Unsigned Stirling numbers of the first kind s(n,7).

1, 28, 546, 9450, 157773, 2637558, 44990231, 790943153, 14409322928, 272803210680, 5374523477960, 110228466184200, 2353125040549984, 52260903362512720, 1206647803780373360, 28939583397335447760

Offset: 7

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

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

Examples

			G.f. = x^7 + 28*x^8 + 546*x^9 + 9450*x^10 + 157773*x^11 + 2637558*x^12 + ...
		

References

• 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).

Links

• 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].

Crossrefs

Cf. A008275 (Stirling1 triangle).

Cf. A000254, A000399, A000454, A000482, A001233, A243569, A243570.

Programs

Maple

A001234 := proc(n) abs(combinat[stirling1](n,7)) ; end: seq(A001234(n),n=7..30) ; # R. J. Mathar, Nov 06 2009

Mathematica

Table[Abs[StirlingS1[n, 7]], {n, 7, 40}] (* Jean-François Alcover, Mar 24 2020 *)

PARI

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

Sage

[stirling_number1(i,7) for i in range(7,22)] # Zerinvary Lajos, Jun 27 2008

Formula

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]

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

Extensions

More terms from R. J. Mathar, Nov 06 2009