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A001552
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a(n) = 1^n + 2^n + ... + 5^n.
(Formerly M3863 N1584)
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11
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5, 15, 55, 225, 979, 4425, 20515, 96825, 462979, 2235465, 10874275, 53201625, 261453379, 1289414505, 6376750435, 31605701625, 156925970179, 780248593545, 3883804424995, 19349527020825, 96470431101379, 481245667164585, 2401809362313955, 11991391850823225
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OFFSET
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0,1
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COMMENTS
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a(n)*(-1)^n, n>=0, gives the z-sequence for the Sheffer triangle A049460 ((signed) 5-restricted Stirling1 numbers), which is the inverse triangle of A193685 (5-restricted Stirling2 numbers). See the W. Lang link under A006232 for a- and z-sequences for Sheffer matrices. The a-sequence for each (signed) r-restricted Stirling1 Sheffer triangle is A027641/A027642 (Bernoulli numbers). - Wolfdieter Lang, Oct 10 2011
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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. 813.
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) = Sum_{k=1..5} k^n, n >= 0.
O.g.f.: (5 - 60*x + 255*x^2 - 450*x^3 + 274*x^4)/Product_{j=1..5} (1 - j*x). - Simon Plouffe in his 1992 dissertation
E.g.f.: exp(x)*(1-exp(5*x))/(1-exp(x)) = Sum_{j=1..5} exp(j*x) (trivial). - Wolfdieter Lang, Oct 10 2011
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MATHEMATICA
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Table[Total[Range[5]^n], {n, 0, 40}] (* T. D. Noe, Oct 10 2011 *)
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PROG
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(PARI) a(n)=if(n<0, 0, sum(k=1, 5, k^n))
(Sage) [3**n + sigma(4, n) + 5**n for n in range(22)] # Zerinvary Lajos, Jun 04 2009
(Sage) [1 + 2**n + 3**n + 4**n + 5**n for n in range(22)] # Zerinvary Lajos, Jun 04 2009
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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