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A000481
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Stirling numbers of the second kind, S(n,5).
(Formerly M4981 N2141)
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14
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1, 15, 140, 1050, 6951, 42525, 246730, 1379400, 7508501, 40075035, 210766920, 1096190550, 5652751651, 28958095545, 147589284710, 749206090500, 3791262568401, 19137821912055, 96416888184100, 485000783495250, 2436684974110751, 12230196160292565, 61338207158409090
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OFFSET
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5,2
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REFERENCES
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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).
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LINKS
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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
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a(n) = A008277(n, 5) (Stirling2 triangle).
G.f.: x^5/product(1-k*x, k=1..5).
E.g.f.: ((exp(x)-1)^5)/5!.
a(n) = sum(sum(binomial(k,r)*(15)^(k-r)*sum((-85)^(r-m)*binomial(r,m)*sum(binomial(m,j)*binomial(j,n-m-k-j-r)*(225)^(m-j)*(-274)^(r+m+k+2*j-n)*(120)^(n-m-k-j-r),j,0,m),m,0,r),r,0,k),k,1,n), n>0. - Vladimir Kruchinin, Aug 30 2010
a(n) = det(|s(i+5,j+4)|, 1 <= i,j <= n-5), where s(n,k) are Stirling numbers of the first kind. - Mircea Merca, Apr 06 2013
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MAPLE
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A000481:=-1/(z-1)/(4*z-1)/(-1+3*z)/(2*z-1)/(5*z-1); # conjectured by Simon Plouffe in his 1992 dissertation
a := n -> (1-4^n+2*(3^n-2^n)+5^(n-1))/24:
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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