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Search: id:A007778
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| 0, 1, 8, 81, 1024, 15625, 279936, 5764801, 134217728, 3486784401, 100000000000, 3138428376721, 106993205379072, 3937376385699289, 155568095557812224, 6568408355712890625, 295147905179352825856
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Number of edges of the complete bipartite graph of order n+n^n, K_n,n^n - Roberto E. Martinez II (remartin(AT)fas.harvard.edu), Jan 07 2002
All rational solutions to the equation x^y = y^x, with x < y, are given by x = A000169(n+1)/A000312(n), y = A000312(n+1)/A007778(n), where n = 1, 2, 3, ... . - Nick Hobson Nov 30 2006
a(n) is also the number of ways of writing an n-cycle as the product of n+1 transpositions. [From Nikos Apostolakis (nikos.ap(AT)gmail.com), Nov 22 2008]
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REFERENCES
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Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005; see p. 67.
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LINKS
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N. Hobson, Exponential equation.
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FORMULA
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E.g.f.: -W(-x)/(1+W(-x))^3, W(x) Lambert's function (principal branch).
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MAPLE
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a:=n->mul(n, k=0..n): seq(a(n), n=0..16); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 26 2008
restart:a:=n->mul(sum(1, j=1..n), k=0..n): seq(a(n), n=0..16); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 01 2009]
with(finance):seq(futurevalue(1, n-2, n), n=1..17); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 25 2009]
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MATHEMATICA
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lst={}; Do[a=n^(n+1); AppendTo[lst, a], {n, 0, 2*4!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 01 2008]
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CROSSREFS
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Cf. A000169, A000272, A000312, A007830, A008785-A008791. Essentially the same as A065440.
Sequence in context: A098308 A055996 A068617 this_sequence A065440 A092366 A022519
Adjacent sequences: A007775 A007776 A007777 this_sequence A007779 A007780 A007781
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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