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A008788
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a(n) = n^(n+2).
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13
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0, 1, 16, 243, 4096, 78125, 1679616, 40353607, 1073741824, 31381059609, 1000000000000, 34522712143931, 1283918464548864, 51185893014090757, 2177953337809371136, 98526125335693359375, 4722366482869645213696
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..200
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
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E.g.f.(x): T*(1 + 2*T)*(1-T)^(-5); where T=T(x) is Euler's tree function (see A000169). - Len Smiley, Nov 17 2001
See A008517 and A134991 for similar e.g.f.s. and A048993. - Tom Copeland, Oct 03 2011
E.g.f.: d^2/dx^2 {x^2/(T(x)^2*(1-T(x))}, where T(x) = sum {n >= 1} n^(n-1)*x^n/n! is the tree function of A000169. - Peter Bala, Aug 05 2012
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EXAMPLE
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G.f. = x + 16*x^2 + 243*x^3 + 4096*x^4 + 78125*x^5 + 1679616*x^6 + ...
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MAPLE
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a:=n->add(add(mul(add(1, i=0..n), j=0..n), k=0..n), m=0..n): seq(a(n), n=-1..19); # Zerinvary Lajos, Jun 16 2007
a:=n->mul(n, k=-1..n):seq(a(n), n=0..20); # Zerinvary Lajos, Jan 26 2008
with(finance):seq(futurevalue(1, n-3, n), n=2..22); # Zerinvary Lajos, Mar 25 2009
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MATHEMATICA
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Table[n^(n+2), {n, 0, 20}] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)
CoefficientList[Series[LambertW[-x] * (2*LambertW[-x]-1) / (1 + LambertW[-x])^5, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Dec 20 2014 *)
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PROG
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(MAGMA) [n^(n+2): n in [0..20]]; // Vincenzo Librandi, Jun 11 2013
(PARI) vector(20, n, (n-1)^(n+1)) \\ G. C. Greubel, Nov 14 2017
(Sage) [n^(n+2) for n in (0..20)] # G. C. Greubel, Sep 11 2019
(GAP) List([0..20], n-> n^(n+2)); # G. C. Greubel, Sep 11 2019
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CROSSREFS
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Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008789, A008790, A008791.
Sequence in context: A119933 A274753 A207995 * A219671 A138460 A182148
Adjacent sequences: A008785 A008786 A008787 * A008789 A008790 A008791
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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