A000771 Stirling numbers of second kind, S(n,7). (Formerly M5201 N2263)

1, 28, 462, 5880, 63987, 627396, 5715424, 49329280, 408741333, 3281882604, 25708104786, 197462483400, 1492924634839, 11143554045652, 82310957214948, 602762379967440, 4382641999117305, 31677463851804540, 227832482998716310, 1631853797991016600

Offset

7,2

Comments

G.f.: x^7/product(1-k*x,k=1..7). E.g.f.: ((exp(x)-1)^7)/7!.

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. 835.

F. N. David, M. G. Kendall and D. E. Barton, Symmetric Function and Allied Tables, Cambridge, 1966, p. 223.

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..200

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].

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 350

Index entries for linear recurrences with constant coefficients, signature (28,-322,1960,-6769,13132,-13068,5040).

Formula

a(n) = A008277(n, 7) (Stirling2 triangle).

a(n) = 1/720*(7^(n-1)-6^n+3*5^n-5*4^n+5*3^n-3*2^n+1). - Vaclav Kotesovec, Nov 19 2012

a(n) = det(|s(i+7,j+6)|, 1 <= i,j <= n-7), where s(n,k) are Stirling numbers of the first kind. - Mircea Merca, Apr 06 2013

Mathematica

lst={}; Do[f=StirlingS2[n, 7]; AppendTo[lst, f], {n, 7, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 27 2008 *)
CoefficientList[Series[1/((1 - x) (1 - 2 x) (1 - 3 x) (1 - 4 x) (1 - 5 x) (1 - 6 x) (1 - 7 x)), {x, 0, 25}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 20 2011 *)
Table[1/720*(7^(n-1)-6^n+3*5^n-5*4^n+5*3^n-3*2^n+1), {n, 7, 20}] (* Vaclav Kotesovec, Nov 19 2012 *)
LinearRecurrence[{28, -322, 1960, -6769, 13132, -13068, 5040}, {1, 28, 462, 5880, 63987, 627396, 5715424}, 20] (* or *) Drop[StirlingS2[Range[30], 7], 6] (* Harvey P. Dale, Jul 25 2021 *)

Crossrefs

Cf. A008277.

Sequence in context: A007833 A080315 A022752 * A327508 A215767 A079518

Adjacent sequences: A000768 A000769 A000770 * A000772 A000773 A000774

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Two more terms from Neven Juric, Oct 22 2009

Definition corrected by Vaclav Kotesovec, Nov 19 2012

Status

approved