A001234 Unsigned Stirling numbers of the first kind s(n,7). (Formerly M5202 N2264)

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

Offset

7,2

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

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].

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A008275 (Stirling1 triangle).

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

Sequence in context: A163198 A278190 A346322 * A145149 A062142 A240800

Adjacent sequences: A001231 A001232 A001233 * A001235 A001236 A001237

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

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

Status

approved