1,2

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

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

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

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.

T. D. Noe, Table of n, a(n) for n=1..1000

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].

S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.

A. F. Labossiere, Sobalian Coefficients.

A. F. Labossiere, Miscellaneous.

Eric Weisstein's World of Mathematics, Stirling numbers of the 2nd kind.

G.f. : x(1+22x+58x^2+24x^3)/(1-x)^9 - Paul Barry (pbarry(AT)wit.ie), Aug 05 2004

a(n) = Stirling2(n+4, n) = Sum(Sum(Sum(Sum(i*j*k*l, i = 1 .. j), j = 1 .. k), k = 1 .. l), l = 1 .. n) = n*(n+4)*(n+3)*(n+2)*(n+1)*(15*n^3+30*n^2+5*n-2)/5760. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 31 2005

E.g.f. with offset -3: exp(x)*(1*(x^4)/4! + 26*(x^5)/5! + 130*(x^6)/6! + 210*(x^7)/7! +105*(x^8)/8!). For the coefficients [1, 26, 130, 210, 105] see triangle A112493. E.g.f.: x*exp(x)*(15*x^7+600*x^6+8600*x^5+55248*x^4+162960*x^3+202560*x^2+83520*x+5760)/5760. Above given e.g.f. differentiated three times.

A001298:=-(1+22*z+58*z**2+24*z**3)/(z-1)**9; [Conjectured by S. Plouffe in his 1992 dissertation.]

lst={}; Do[f=StirlingS2[n, n-4]; AppendTo[lst, f], {n, 4, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]

(Other) sage: [stirling_number2(n, n-4) for n in xrange(5, 24)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]

Cf. A008277, A094262, A001296, A001297.

Sequence in context: A161558 A156094 A115151 this_sequence A027841 A000500 A141912

Adjacent sequences: A001295 A001296 A001297 this_sequence A001299 A001300 A001301

nonn

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