1,1

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. 833.

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. 226.

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].

A. F. Labossiere, Sobalian Coefficients.

A. F. Labossiere, Miscellaneous.

a(n) = binomial(n+4, 5)*(15*n^3+150*n^2+485*n+502)/48 - Andre F. Labossiere (boronali(AT)laposte.net), Sep 30 2004

Stirling1(n+1, n-3) = Sum(Sum(Sum(Sum(i*j*k*l, i = j+1 .. n), j = k+1 .. n), k = l+1 .. n), l = 1 .. n), cf. A001298. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 31 2005

E.g.f. with offset 4: exp(x)*(sum(A112486(4, m)*(x^(4+m))/(4+m)!, m=0..4)).

a(n)= (f(n+3, 4)/8!)*sum(A112486(4, m)*f(8, 4-m)*f(n-1, m), m=0..min(4, n-1)), with the falling factorials f(n, m):=n*(n-1)*...*(n-(m-1)).

G.f.: x*(24+58*x+22*x^2+x^3)/(1-x)^9, see the k=3 row of triangle A112007 for [24, 58, 22, 1].

(Other) sage: [stirling_number1(n, n-4) for n in xrange(5, 30)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]

Cf. A094216.

Sequence in context: A001413 A022065 A125412 this_sequence A006665 A010940 A045854

Adjacent sequences: A000912 A000913 A000914 this_sequence A000916 A000917 A000918

nonn

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

More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 17 2000