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A007550 Natural numbers exponentiated twice.
(Formerly M3568)
9

%I M3568

%S 1,4,20,127,967,8549,85829,962308,11895252,160475855,2343491207,

%T 36795832297,617662302441,11031160457672,208736299803440,

%U 4169680371133507,87648971646028515,1933298000313801349,44633323736412392093,1076069422794010119112

%N Natural numbers exponentiated twice.

%C The subsequence of primes (for n = 4, 5, 7) begins: 127, 967, 85829. The subsequence of semiprimes (for n = 2, 6) begins: 4, 8549. - _Jonathan Vos Post_, Feb 09 2011

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Alois P. Heinz, <a href="/A007550/b007550.txt">Table of n, a(n) for n = 1..200</a>

%H M. Bernstein and N. J. A. Sloane, <a href="http://arXiv.org/abs/math.CO/0205301">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to arXiv version]

%H M. Bernstein and N. J. A. Sloane, <a href="/A003633/a003633_1.pdf">Some canonical sequences of integers</a>, Linear Alg. Applications, 226-228 (1995), 57-72; erratum 320 (2000), 210. [Link to Lin. Alg. Applic. version together with omitted figures]

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=166">Encyclopedia of Combinatorial Structures 166</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

%F E.g.f.: exp(G(x) - 1) - 1, where G(x) = exp(x*exp(x)) = e.g.f. for A000248; clarified by _Ilya Gutkovskiy_, Jun 25 2018

%F a(n) = sum( k^(n - k) binomial(n,k) bell(k), k = 0..n ). - _Olivier Gérard_, Oct 24 2007

%p exptr:= proc(p) local g; g:= proc(n) option remember; p(n) +add(binomial(n-1, k-1) *p(k) *g(n-k), k=1..n-1) end: end: a:= exptr(exptr(n->n)): seq(a(n), n=1..30); # _Alois P. Heinz_, Oct 07 2008

%t a[n_] := Sum[k^(n-k)*Binomial[n, k]*BellB[k], {k, 0, n}]; Table[a[n], {n, 1, 20}] (* _Jean-François Alcover_, Feb 11 2014, after _Olivier Gérard_ *)

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_

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Last modified April 13 19:42 EDT 2021. Contains 342941 sequences. (Running on oeis4.)