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A000915
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Stirling numbers of first kind s(n+4,n).
(Formerly M5155 N2239)
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7
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24, 274, 1624, 6769, 22449, 63273, 157773, 357423, 749463, 1474473, 2749747, 4899622, 8394022, 13896582, 22323822, 34916946, 53327946, 79721796, 116896626, 168423871, 238810495, 333685495, 460012995, 626334345, 843041745
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| It appears that the definition of this sequence should be changed to s(n+4,n) or the offset changed to 5.(see Lajos code). A simlar error in defintion is found in A001303..(s(n+3,n)). Gary Detlefs
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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. 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.
R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 2nd. ed., 1994, p. 259.
J. Riordan, An Introduction to Combinatorial Analysis, Wiley, 1958, p. 48.
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).
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LINKS
| 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].
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FORMULA
| 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].
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PROG
| (Other) sage: [stirling_number1(n, n-4) for n in xrange(5, 30)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009]
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CROSSREFS
| Cf. A008275, A094216.
Sequence in context: A022065 A125412 A187048 * A006665 A010940 A045854
Adjacent sequences: A000912 A000913 A000914 * A000916 A000917 A000918
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 17 2000
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