0,3

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).

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.

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 227, #16.

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.

(n^2-5n+6)C(n, 4)/2.

G.f. : x(1+8x+6x^2)/(1-x)^7 - Paul Barry (pbarry(AT)wit.ie), Aug 05 2004

C(n+4, n)*C(n+2, 2) - Zerinvary Lajos (zlaja(AT)freemail.hu), Apr 27 2005

E.g.f. with offset -2: exp(x)*(1*(x^3)/3! + 11*(x^4)/4! + 25*(x^5)/5! + 15*(x^6)/6!). For the coefficients [1, 11, 25, 15] see triangle A112493. E.g.f.: 1/48*x*exp(x)*(x^5+22*x^4+152*x^3+384*x^2+312*x+48)/48. Above given e.g.f. differentiated twice.

((binomial(n+6,n+1)-binomial(n+5,n))*((binomial(n+4,n+1)-binomial(n+3,n))). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 12 2006

A001297:=-(1+8*z+6*z**2)/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]

lst={}; Do[f=StirlingS2[n, n-3]; AppendTo[lst, f], {n, 3, 5!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 27 2008]

(Other) sage: [stirling_number2(n, n-3) for n in xrange(3, 34)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]

Cf. A008277, A094262, A001296, A001298, A008277, A048993, A062196.

Sequence in context: A010822 A022707 A151974 this_sequence A005716 A048630 A035163

Adjacent sequences: A001294 A001295 A001296 this_sequence A001298 A001299 A001300

nonn,easy

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

More terms from Gerald McGarvey (Gerald.McGarvey(AT)comcast.net), Jul 18 2004

Initial zero added by N. J. A. Sloane (njas(AT)research.att.com), Jan 21 2008